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Color image segmentation based on 3-D clustering
Abstract
In this paper, a new segmentation algorithm for color images based on mathematical morphology is presented. Color image segmentation is essentially a clustering process in 3-D color space, but the characteristics of clusters vary severely, according to the type of images and color coordinates. Hence, the methodology employs the scheme of thresholding the difference of Gaussian smoothed 3-D histogram to get the initial seeds for clustering, and then uses a closing operation and adaptive dilation to extract the number of clusters and their representative values, and to include the suppressed bins during Gaussian smoothing, without a priori knowledge on the image. This procedure also implicitly takes into account the statistical properties, such as the shape, connectivity and distribution of clusters. Intensive computer simulation has been performed and the results are discussed in this paper. The results of the simulation show that the proposed segmentation algorithm is independent of the choice of color coordinates, the shape of clusters, and the type of images. The segmentation results using the k-means technique are also presented for comparison purposes.
... Teori himpunan digunakan untuk menggambarkan struktur geometris secara statistik. Morfologi matematika sekarang banyak digunakan dalam visi komputer, analisis gambar, dan aplikasi pengenalan pola seperti segmentasi gambar berwarna dalam ruang 3-D [4], metode deteksi tepi citra penginderaan jauh [5], dan pemrosesan citra medis [6], di antara yang lain. Prinsip utama di balik morfologi matematika adalah menggunakan elemen struktural dengan ketajaman tertentu untuk mengukur dan mendeteksi objek yang terkait. ...
... Dalam morfologi matematika fuzzy, rumus untuk mendeteksi tepi dari citra daun tembakau adalah 5. Hasil dari dilasi fuzzy adalah X, sedangkan pengembangan dari erosi fuzzy adalah Y. Baik X dan Y berasal dari ide yang sama, yang terstruktur oleh elemen yang sama. Setelah itu, X dan Y dibandingkan (5). d1 dan d2 adalah dua nilai maksimum antara piksel yang sesuai di X dan Y di dalam jendela 3*3 yang berpusat pada piksel I j), dan perbedaan (i, j) dihitung pada piksel yang sesuai di (5). ...
... Setelah itu, X dan Y dibandingkan (5). d1 dan d2 adalah dua nilai maksimum antara piksel yang sesuai di X dan Y di dalam jendela 3*3 yang berpusat pada piksel I j), dan perbedaan (i, j) dihitung pada piksel yang sesuai di (5). (aku j). ...
Ekstraksi tepi pada foto daun merupakan langkah penting dalam pemeriksaan daun terkomputerisasi. Sangat penting untuk mendeteksi tepi dan menyimpan informasi tekstur rinci tentang daun, seperti urat dan warna. Sebuah kamera digital menangkap gambar daun asli. Fungsi keanggotaan digunakan untuk memproses daun yang diperoleh. Tepi tersebut kemudian dideteksi menggunakan pendekatan morfologi fuzzy matematis [1]. Membandingkan hasil teknik deteksi tepi yang ada seperti morfologi biner dan Sobel di bawah berbagai pengaturan menunjukkan efisiensi deteksi tepi berdasarkan morfologi matematika fuzzy.
... Clearly all of the above clustering strategies can be generalized from the clustering of 3-element vectors encoding a single color to more general notions of features, which could include information about texture [18], pixel location [18,111] or surrounding pixel values [148]. Park et al. use morphology to expand color clusters nonlinearly in feature space [111]. ...
... Clearly all of the above clustering strategies can be generalized from the clustering of 3-element vectors encoding a single color to more general notions of features, which could include information about texture [18], pixel location [18,111] or surrounding pixel values [148]. Park et al. use morphology to expand color clusters nonlinearly in feature space [111]. ...
... The most notable drawback of color clustering methods [89,111,134,148] is that they normally do not take any spatial relationships into account, and determine the segmentation strictly on a pixel-by-pixel basis, normally using the Euclidean distance. We will demonstrate for the problems of our interest, specifically the segmentation of images involving illumination effects, some degree of spatial dependence is crucial in formulating an adequate approach. ...
... The partitioning approaches gradually lost their importance after the introduction of soft computing techniques. Most of the segmentation techniques provide approximate solution to the image segmentation problem, especially when applied to color image segmentation [4,5,6]. They further need optimization for enhancing the segmentation performance [7]. ...
... The non uniform sampling of color space considering the physiological limitations of human color vision results in reduction in number of shades of colors resulting in uniform JND color space. The reduction in number of colors leads to reduction of search space and hence improves convergence time considerably [12].Thus, the new space formed is perceptually uniform and has the advantages of uniform spaces in image analysis [5]. The color image segmentation technique in HSI color space by using JND is presented in [15]. ...
... Extension des méthodes par histogrammes, la cohérence d'un pixel définie par Pass en 1996 [Pass et al., 1996] est le degré d'appartenance de la couleur à de larges régions spatiales couleur homogènes. Pour chaque couleur de l'histogramme, un vecteur de cohérence est alors défini par le nombre de pixels cohérents et par le nombre de pixels incohérents. ...
... Pourtant un nuage couleur peut être séparable en 3 dimensions sans l'être de manière évidente sur un seul axe. Les méthodes les plus classiques utilisent une détection de pics dans l'histogramme 3D, souvent par une approche morphologique [Park et al., 1998]. Ceci permet ensuite de séparer les pixels entre ces pics. ...
The matter of this work is content based image retrieval and more precisely the contribution
of the low level methods.
After having discussed the various existing approaches, we recall the semantic gap between
the user expectations and what really the systems of research propose. Most of these approaches
rely on a preliminary step of segmentation whose validity and robustness must be studied. Then
we propose a protocol of evaluation and a practical example of benchmarks. The originality
consists in not comparing a segmentation with a theoretical reference but judging its stability
objectively.
The third part of this document introduces three specific contributions likely to improve the
chain of research. Initially, a detector of blur allows to extract a meta-data carried by the image:
the unblur regions, a priori of focusing. Secondly, we expose a descriptor based on the extraction
of emergent areas using only the color criteria. This process, combined with adapted distances,
may allow for example a color pre-filtering before the step of similarity research . Finally, we
briefly introduce an algebra of histograms able as well as possible to exploit the information
contained in this type of descriptors, via a specific query language.
... (a) if δ(c i , x j ) < jndc i , then update the membership of x j inF i at t + 1 iteration by µF i (x j )(t + 1) = 1.0 (15) (b) if δ(c k , x j ) < jndc k , for k = i,c k ∈C then update the membership of x j inF i at t + 1 iteration by µF i (x j )(t + 1) = 0.0 (16) (c) if condition (a) and (b) are not satisfied for all c k ∈C, k = 1..c, then update the membership of x j inF i at t + 1 iteration by ...
The research interest of this paper is focused on the efficient clustering task for an arbitrary color data. In order to tackle this problem, we have tried to model the inherent uncertainty and vagueness of color data using fuzzy color model. By taking fuzzy approach to color modeling, we could make a soft decision for the vague regions between neighboring colors. The proposed fuzzy color model defined a three dimensional fuzzy color ball and color membership computation method with two inter-color distances. With the fuzzy color model, we developed a new fuzzy clustering algorithm for an efficient partition of color data. Each fuzzy cluster set has a cluster prototype which is represented by fuzzy color centroid.
... Histopatolojik görüntülerin bölütlenmesinde gerçekleştirilen çalışmalar CNN tabanlı eğitim mimarilerini kullanmayan klasik yöntemler ve derin öğrenme tabanlı yöntemler olarak iki sınıfta incelenebilir. Kmeans [1], morphology [2], watershed [3], thresholding [4], Active Contour Models (ACM) [5] gibi yöntemler bölütleme alanında kullanılan klasik yöntemlerdendir. ...
... A hybrid color space based approach is suggested in [34]. Using morphological analysis of color histogram, a segmentation algorithm is presented in [20], where the authors conclude that segmentation results are similar for five different color spaces. In [6], a comparison of ten color spaces for skin detection and segmentation is presented. ...
Archaic manuscripts are an important part of ancient civilization. Unfortunately, such documents are often affected by various age related degradations, which impinge their legibility and information contents, and destroy their original look. In general, these documents are composed of three layers of information: foreground text, background, and unwanted degradation in the form of patterns interfering with the main text. In this work, we are presenting a color space based image segmentation technique to separate and remove the bleed-through degradation in digital ancient manuscripts. The main theme is to improve their readability and restore their original aesthetic look. For each pixel, a feature vector is created using color spectral and spatial location information. A pixel based segmentation method using Gaussian Mixture Model (GMM) is employed, assuming that each feature vector corresponds to a Gaussian distribution. Based on this assumption, each pixel is supposed to be drawn from a mixture of Gaussian distribution, with unknown parameters. The Expectation-Maximization (EM) approach is then used to estimate the unknown GMM parameters. The appropriate class label for each pixel is then estimated using posterior probability and GMM parameters. Unlike other binarization based document restoration method where the focus is on text extraction, we are more interested in restoring the aesthetically pleasing look of the ancient documents.The experimental results validate the usefulness of proposed method in terms of successful bleed-through identification and removal, while preserving foreground-text and background information.
... As mention earlier the machine learning technique used is unsupervised, which is used for drawing certain inferences from datasets consisting of input data without labelled responses. The algorithm used is K-means [4,11] which is a partition-based cluster analysis method and it is very effective algorithm for finding clusters for a given dataset. Park et al. [12] applied this algorithm to a pattern space representation of RGB coordinates. ...
Remote sensing data and satellite images are broadly used for land cover information. There are so many challenges to classify pixels on the basis of features and characteristics. Generally it is pixel classification that required the count of pixels for certain area of interest. In the proposed model, we are applying unsupervised machine learning to classify the content of the input images on the basis of pixels intensity. The study aims to compare classification accuracy of different landscape characteristics like water, forest, urban, agricultural areas, transport network and other classes adapted from CORINE (Coordination of information on the environment) nomenclature. To fulfil the aim of the model, accessing data from Google map using Google static API service which creates a map based on URL parameters sent through a standard HTTP (Hyper Text Transfer Protocol) request and returns the map as an image which can be display on any graphical user interface platform. The Google Static Maps API returns an image either in GIF, PNG or JPEG format in response to an HTTP request. To identify different land cover/use classes using k-means clustering. The model is dynamic in nature that describes the clustering as well formulate the area of the concerned class or clustered fields.
... Most of the works in the literature using 3D histograms do not take into account theses characteristics and they divide the space by means of rigid structures such as hyperrectangles or spheres [7,43,9]. Other works, such as [33] and [34], take into account the statistical properties, such as shape and distribution of the clusters in the histogram. The main drawback of these latter methods is that they do not have a sound theoretical background. ...
We present a method for the automatic estimation of the minimum set of colors needed to describe an image. We call this minimal set “color palette”. The proposed method combines the well-known K-Means clustering technique with a thorough analysis of the color information of the image. The initial set of cluster seeds used in K-Means is automatically inferred from this analysis. Color information is analyzed by studying the 1D histograms associated to the hue, saturation and intensity components of the image colors. In order to achieve a proper parsing of these 1D histograms a new histogram segmentation technique is proposed. The experimental results seem to endorse the capacity of the method to obtain the most significant colors in the image, even if they belong to small details in the scene. The obtained palette can be combined with a dictionary of color names in order to provide a qualitative image description.
... The classes for color segmentation are built by means of a cluster identification scheme which is performed either by an analysis of the color histogram [4] or by a cluster analysis procedure [5]. When the classes are constructed, the pixels are assigned to one of them by means of a decision rule and then mapped back to the original image plane to produce the segmentation. ...
Color segmentation in digital images is a challenging task due to image capture conditions. Typical segmentation algorithms present several difficulties in this process because they do not tolerate variations in color hue corresponding to the same object. In this chapter is presented an approach for color segmentation based on learning vector quantization (LVQ) networks, which conducts the segmentation process by means a color-based pixel classification. In the LVQ networks, neighboring neurons have the capability to learn how to recognize close sections of the input space. The presented segmentation approach classifies the pixels directly by means of the LVQ network. The experimental results over a set of images show the efficiency of the LVQ-based method to satisfactorily segment color despite remarkable illumination problems.
... The classes for color segmentation are built by means of a cluster identification scheme which is performed either by an analysis of the color histogram [4] or by a cluster analysis procedure [5]. When the classes are constructed, the pixels are assigned to one of them by means of a decision rule and then mapped back to the original image plane to produce the segmentation. ...
Segmentation in color images is a complex and challenging task in particular to overcome changes in light intensity caused by noise and shadowing. Most of the segmentation algorithms do not tolerate variations in color hue corresponding to the same object. By means of the Learning Vector Quantization (LVQ) networks, neighboring neurons are able to learn how to recognize close sections of the input space. Neighboring neurons would thus correspond to color regions illuminated in different ways. This chapter presents an image segmentator approach based on LVQ networks which considers the segmentation process as a color-based pixel classification. The segmentator operates directly upon the image pixels using the classification properties of the LVQ networks. The algorithm is effectively applied to process sampled images showing its capacity to satisfactorily segment color despite remarkable illumination differences.
... Image segmentation, which partitions an image into a certain number of regions according to the similarity of the image pixels, is crucial for multimedia applications such as the indexing of images or the tracking of objects in videos. The K-means clustering algorithm has been widely used for the purpose of image segmentation [13,14]. We apply this algorithm to segment images using the RGB colour space where each pixel is represented by a 3-dimensional vector. ...
In this paper, a K-means clustering algorithm with flexible hardware/software co-design is reported for machine learning and multimedia applications such as image recognition and image segmentation. The contributions of this work can be attributed to two aspects. The first is the hardware architecture for nearest neighbour searching, which is used to overcome the main computational cost of a K-means clustering algorithm. The second aspect is the high flexibility with respect to different applications which comes from not only the software but also the hardware. High flexibility with respect to the number of training data samples, the
dimensionality of each sample vector, and the number of clusters, is one of the major shortcomings of dedicated hardware implementations for the K-means algorithm. The K-means algorithm with hardware/software architecture, which is versatile in machine learning, pattern recognition, and multimedia processing, is extendable to embedded systems and mobile devices. We benchmark this work against the
applications of handwritten digit recognition and image segmentation to verify its excellent performance and high flexibility.
... La méthode la plus classique est sans doute l'algorithme des centres mobiles (ou ses variantes les nuées dynamiques et les k-means) qui est grandement utilisé tant dans la quantification vectorielle que dans la compression de données. Il est applicable dans n'importe quel espace colorimétrique : PARK [PARK98] l'emploie dans l'espace RVB alors que WEEKS et HAGUE [WEEKS97] le font dans l'espace HSI. Ces méthodes de classification sont non hiérarchiques. ...
Mme Marinette Revenu, Professeur, université de Caen, GREYC M. Patrick Lambert, Maître de Conférences HDR, université de Savoie, LISTIC M. Ludovic Macaire, Maître de Conférences, université de Lille, I3D M. Jean-Marc Ogier, Professeur, université de la Rochelle, L3I Mme Christine Fernandez-Maloigne, Professeur, université de Poitiers, SIC M. Noël Richard, Maître de Conférences, université de Poitiers, SIC M. Éric Palazzo, Professeur, université de Poitiers, CESCM
... L'analyse vectorielle des histogrammes 3D passe par une binarisation de l'histogramme, suivie d'un étiquetage en composantes connexes, par des techniques de morphologie mathématique [Park et al.,1998], ou par l'algorithme de ligne de partage des eaux [Shafarenko et al. 1998]. Souvent, l'histogramme est filtré avant traitement pour supprimer les maxima locaux [Géraud et al. 2001]. ...
Recent technical progresses supply sensors able to characterize a scene by multicomponent images. Most often, the segmentation of multicomponent images proceeds either through the analysis of their marginal histograms, ignoring the correlation between components, or by requantifying the components due to the difficulty of treating hudge n-dimensional (nD) histograms (n is the number of the image components). In a first step, we have developed a vectorial unsupervised and non parametric segmentation of multicomponent images (n ≥ 3), which is based on the hierarchical analysis of the compact nD histograms (an algorithmic data structure which diminishes the histogram size without losses). The modes of the histogram are obtained by labelling its connected components. The segmentation results are compared to those supplied by the classical K-means method, by using the criterions of Levine-Nazif, Zeboudj, Borsotti or Rosenberger. In a second step, to avoid the over-segmentation resulting from the diffuse character of the nD histograms, we propose to label their connected components in a fuzzy manner. The results are compared to those obtained by a requantification of the histogram. Thus we dispose of four segmentation strategies, and we compare their results on a set of natural as well as synthetic images. At last, this work is used to analyze histological cuts of apples in optical microscopy. The results show differences between three apples species, in relation with texture and firmness analyses.
... Colour image segmentation is a complex but crucial task having application in several areas. Two most popular techniques for colour image segmentation include histogram-based methods [5] and neighbourhood based segmentation [6,7]. ...
Due to the complexity of underlying data in a color image, retrieval of specific object features and relevant information becomes a complex task. Colour images have different color components and a variety of colour intensity which makes segmentation very challenging. In this paper we suggest a fitness function based on pixel-by-pixel values and optimize these values through evolutionary algorithms like differential evolution (DE), particle swarm optimization (PSO) and genetic algorithms (GA). The corresponding variants are termed GA-SA, PSO-SA and DE-SA; where SA stands for Segmentation Algorithm. Experimental results show that DE performed better in comparison of PSO and GA on the basis of computational time and quality of segmented image.
... Since the work of Donoho & Johnstone [4], [5], [6], [7], there has been much research on finding thresholds, however few are specifically designed for images. In this paper, a near optimal threshold estimation technique for image denoising is used which is sub band dependent i.e. the parameters for computing the threshold are estimated from the observed data, one set for each sub band, Markov Random Fields (MRF's) is a commonly used method in the neighborhood-based approach [8], [9]. ...
Segmentation of a color image composed of different kinds of regions can be a hard problem, namely to compute for an exact texture fields. The decision of the optimum number of segmentation areas in an image when it contains similar and/or un stationary texture fields. A novel neighborhood-based segmentation approach is proposed. A genetic algorithm is used in the proposed segment-pass optimization process. In this pass, an energy function, which is defined based on Markov Random Fields, is minimized. In this paper we use an adaptive threshold estimation method for image thresholding in the wavelet domain based on the generalized Gaussian distribution (GGD) modeling of sub band coefficients. This method called Normal Shrink is computationally more efficient and adaptive because the parameters required for estimating the threshold depend on sub band data energy that used in the pre-stage of segmentation. A quad tree is employed to implement the multi resolution framework, which enables the use of different strategies at different resolution levels, and hence, the computation can be accelerated. The experimental results using the proposed segmentation approach are very encouraging.
... La técnica de segmentación del histograma por línea divisoria de aguas, introducida en Watson (1987), fue desarrollada por Soille (1996) para la partición morfológica de imágenes satélite multiespectrales. Después se han propuesto diferentes variantes (Postaire et al., 1993;Petrou et al., 1998;Sang et al. 1998;Park et al. 1998; Géraud et al., 2001), así como otras aplicaciones tal que la detección de caras en imágenes color (Albiol et al., 2001). ...
The choice of a suitable colour space representation is still a challenging task in the processing and analysis of colour images. Starting with the recently proposed family of polar coordinate systems LSH (improving the standard HLS) which have suitable properties for quantitative image processing, the derivation of two bivariate histograms: histr;HS (putting together the Hue component and the Saturation component) and histLS (Luminance and Saturation components) associated to these colour spaces is presented. A method for the morphological clustering of the points in the bivariates histograms is shown, relying on the watershed transformation. Then, by back projecting on the space of the initial colour image, two partitions (chromatic and achromatic) are obtained. A saturationbased combination of the two partitions yields an interesting method for segmenting colour images.
... One of the first attempts was made by Madier et al. [8] in the classification of remotely sensed images. More recently studies, by Soille [14,15] in the segmentation by watershed of features space to land use unsupervised classification, by Muge et al. [10] in a geochemical exploration application to create maps of favorability of occurrence of mineral resources, by Park et al. [11] for colour images segmentation, or by Breen [5] introducing the closing function notion to segment non-image data, have shown the potentialities of using mathematical morphology to model the geometry of complex and irregular training sets of points. ...
In this paper a novel methodology to construct decision region borders that geometrically models the training sets of points is presented. It is shown that with the incorporation of the features of the training sets more correct decision borders are designed and, in consequence,higher classification rates are obtained. This methodology is completely based on mathematical morphology operators and is illustrated with two features (wetness’ tasselled cap and NDVI’s vegetation index) of seven land cover classes (forest (3), soil (2), vegetation and water) constructed from remotely sensed images of a region in centre Portugal.
... Image segmentation, which partitions an image into a certain number of regions according to the similarity of the image pixels, is crucial for multimedia applications such as the indexing of images or the tracking of objects in videos. The K-means clustering algorithm has been widely used for the purpose of image segmentation [32,33]. We apply this algorithm to segment images using the RGB color space where each pixel is represented by a 3-dimensional vector. ...
In this paper, we report a hardware/software (HW/SW) co-designed K-means clustering algorithm with high flexibility and high performance for machine learning, pattern recognition and multimedia applications. The contributions of this work can be attributed to two aspects. The first is the hardware architecture for nearest neighbor searching, which is used to overcome the main computational cost of a K-means clustering algorithm. The second aspect is the high flexibility for different applications which comes from not only the software but also the hardware. High flexibility with respect to the number of training data samples, the dimensionality of each sample vector, the number of clusters, and the target application, is one of the major shortcomings of dedicated hardware implementations for the K-means algorithm. In particular, the HW/SW K-means algorithm is extendable to embedded systems and mobile devices. We benchmark our multi-purpose K-means system against the application of handwritten digit recognition, face recognition and image segmentation to demonstrate its excellent performance, high flexibility, fast clustering speed, short recognition time, good recognition rate and versatile functionality.
... (a) if δ(c i , x j ) < jndc i , then update the membership of x j inF i at t + 1 iteration by µF i (x j )(t + 1) = 1.0 (15) (b) if δ(c k , x j ) < jndc k , for k = i,c k ∈C then update the membership of x j inF i at t + 1 iteration by µF i (x j )(t + 1) = 0.0 (16) (c) if condition (a) and (b) are not satisfied for all c k ∈C, k = 1..c, then update the membership of x j inF i at t + 1 iteration by ...
The research interest of this paper is focused on the efficient clustering task for an arbitrary color data. In order to tackle this problem, we have tried to model the inherent uncertainty and vagueness of color data us- ing fuzzy color model. By taking fuzzy approach to color modeling, we could make a soft decision for the vague regions between neighboring colors. The proposed fuzzy color model defined a three dimensional fuzzy color ball and color membership computation method with two inter-color distances. With the fuzzy color model, we developed a new fuzzy clustering algorithm for an effi- cient partition of color data. Each fuzzy cluster set has a cluster prototype which is represented by fuzzy color centroid. tried to develop a new color model that can represent the color uncertainty and vagueness, which results in a proposed fuzzy color model. We modeled a color space with fuzzy-set theory and created a notion of three di- mensional fuzzy color ball. And we proposed two color distance measures including the distance between a color element and a fuzzy color and the distance between fuzzy colors. With the distance measures, the computation method for color membership value was defined. In order to effectively partition the color data set, fuzzy cluster analysis technique is best choice due to the ability of dealing with color uncertainty. But most of pre- vious fuzzy clustering algorithms were designed for crisp pattern data, thus we need to develop an new algorithm that can tackle the fuzzy data clustering. We applied the proposed fuzzy color model to devise a new approach in fuzzy clustering algorithm. Color is a qualitative feature and we have to make a soft decision in color clustering ac- tivity. Thus each color cluster set is prototyped by color centroid value that is represented by fuzzy color ball. By minimizing the pre-defined evaluation criteria, we could obtain the near-optimal convergence in an iterative color clustering.
A striking feature of micro‐level plant data is the presence of significant variation in factor cost shares across plants within an industry. We develop a methodology based on cluster analysis to decompose cost shares into idiosyncratic and group‐specific components. We apply our methodology to Chilean plant‐level data and find that group‐specific variation accounts for approximately one‐third of the variation in cost shares. We study the implications of these groups in cost shares on the gains from eliminating misallocation. We place bounds on their importance and find that ignoring them can overstate the gains from eliminating misallocation by up to one‐third. This article is protected by copyright. All rights reserved
The exploration of the features presented by the training sets of each class (size, shape and orientation) in order to construct the respective decision regions borders without making explicitly any statistical hypothesis is presented in this paper. Its incorporation allows defining more correct decision borders since there is a significant improvement in the classification rates obtained. Mathematical morphology operators are preferentially used in this methodology, which is illustrated with two spectral features (wetness' tasselled cap and NDVI's vegetation index) of seven land cover classes constructed from Landsat TM satellite images of central Portugal.
A two-layer dendritic lattice neural network is proposed to segment color images in the Red-Green-Blue (RGB) color space. The two layer neural network is a fully interconnected feed forward net consisting of an input layer that receives color pixel values, an intermediate layer that computes pixel interdistances, and an output layer used to classify colors by hetero-association. The two-layer net is first initialized with a finite small subset of the colors present in the input image. These colors are obtained by means of an automatic clustering procedure such as k-means or fuzzy c-means. In the second stage, the color image is scanned on a pixel by pixel basis where each picture element is treated as a vector and feeded into the network. For illustration purposes we use public domain color images to show the performance of our proposed image segmentation technique.
A new color image segmentation approach based on OWT is presented in this work. OWT extracts wavelet features which give a good separation of different patterns. Moreover the proposed algorithm uses morphological operators for effective segmentation. From the qualitative and quantitative results, it is concluded that our proposed method has improved segmentation quality and it is reliable, fast and can be used with reduced computational complexity than direct applications of Histogram Clustering. The main advantage of this method is the use of single parameter and also very faster. While comparing with five color spaces, segmentation scheme produces results noticeably better in RGB color space compared to all other color spaces.
Data clustering is the generic process of splitting a set of datums into a number of homogenous sets. Nevertheless, although a clustering process inputs datums as a set of separate mathematical objects, these entities are in fact correlated within a spatial context specific to the problem class in hand. For example, when the data acquisition process yields a 2D matrix of regularly sampled measurements, as it is the case with image sensors which utilize different modalities, adjacent datums are highly correlated. Hence, the clustering process must take into consideration the spatial context of the datums. A review of the literature, however, reveals that a significant majority of the well-established clustering techniques in the literature ignore spatial context. Other approaches, which do consider spatial context, however, either utilize pre- or post-processing operations or engineer into the cost function one or more regularization terms which reward spatial contiguity. We argue that employing cost functions and constraints based on heuristics and intuition is a hazardous approach from an epistemological perspective. This is in addition to the other shortcomings of those approaches. Instead, in this paper, we apply Bayesian inference on the clustering problem and construct a mathematical model for data clustering which is aware of the spatial context of the datums. This model utilizes a robust loss function and is independent of the notion of homogeneity relevant to any particular problem class. We then provide a solution strategy and assess experimental results generated by the proposed method in comparison with the literature and from the perspective of computational complexity and spatial contiguity.
Image segmentation refers to partitioning an image into different regions that are homogeneous with respect to some image feature. Image segmentation is an important aspect of the human visual perception. Humans use their visual sense to effortlessly partition their surrounding environment into different objects to help recognize them, guide their movements, and for almost every other task in their lives. It is a complex process that includes many interacting components that are involved with the analysis of color, shape, motion, and texture of objects in images. However, for the human visual system, the segmentation of images is a spontaneous, natural activity. Unfortunately it is not easy to create artificial algorithms whose performance is comparable to that of the human visual system. One of the major obstacles to the successful development of theories of segmentation has been a tendency to underestimate the complexity of the problem exactly because the human performance is mediated by methods which are largely subconscious. Because of this, segmentation of images is weakened by various types of uncertainty making most simple segmentation techniques ineffective [1].
A new color image segmentation approach based on OWT is presented in this work. OWT extracts wavelet features which give a good separation of different patterns. Moreover the proposed algorithm uses morphological operators for effective segmentation. From the qualitative and quantitative results, it is concluded that our proposed method has improved segmentation quality and it is reliable, fast and can be used with reduced computational complexity than direct applications of Histogram Clustering. The main advantage of this method is the use of single parameter and also very faster. While comparing with five color spaces, segmentation scheme produces results noticeably better in RGB color space compared to all other color spaces.
This manuscript introduces a new technique for autonomous segmentation of color images in Red-Green-Blue (RGB) space that makes use of lattice auto-associative memories (LAAMs). LAAMs are artificial neural networks able to store a finite set X of pattern vectors and retrieve them almost correctly when a noisy or incomplete input is presented. Two dual lattice auto-associative memories have been established, the min memory WXX and the max memory MXXwhose column vectors, scaled appropriately, are used to determine a tetrahedron enclosing a subset of X. Specifically, the column vectors of each memory will correspond to the most saturated color pixels. Thus, from the perspective of convex set geometry, the scaled column vectors of a LAAM are extreme points of a convex subset of X (tetrahedron), and any other pixel can be considered a linear mixture of these points. Unsupervised segmentation of a color image is then realized by unmixing pixels using the non-negative least square method. We provide illustrative examples to demonstrate the effectiveness of our method as well as segmentation results for some RGB color images.
A novel ultrasound image segmentation algorithm, which is based on the spectral cluster ensemble, is proposed to segment ultrasound images with low SNR. Firstly, the improved total variation model is used to eliminate noise in ultrasound. Then cluster ensemble approach which integrates K-means clusters and improved spectral cluster algorithm, is applied to segment ultrasound images. At last, the segmentation result is clustered again using K-means cluster to get the ultimate segmentation result. A large amount of experimental results have proved that our method outperforms many state-of-arts methods in the aspect of segmentation.
In this work, we develop a statistical framework for data clustering which uses hierarchical Dirichlet processes and Beta-Liouville distributions. The parameters of this framework are leaned using two variational Bayes approaches. The first one considers batch settings and the second one takes into account the dynamic nature of real data. Experimental results based on a challenging problem namely visual scenes categorization demonstrate the merits of the proposed framework.
Fuzzy C-means (FCM) is an unsupervised clustering technique that is often used for the unsupervised segmentation of multivariate images. In traditional FCM the clustering is based on spectral information only and the geometrical relationship between neighbouring pixels is not used in the clustering procedure. In this paper, the spatially guided FCM (SG-FCM) algorithm is presented which segments multivariate images by incorporating both spatial and spectral information. Spatial information is described by a geometrical shape description and can vary from a local neighbourhood to a more extended shape model such as Hough circle detection. A modified FCM objective function uses the spatial information as described by the shape model. This results in a segmented image in which the construction of the cluster prototypes is influenced by spatial information. The performance of SG-FCM is compared with both FCM and the sequence of FCM and a majority filter. The SG-FCM segmented image shows more homogeneous regions and less spurious pixels. Copyright © 2003 John Wiley & Sons, Ltd.
This paper describes a new approach to geometrically guided fuzzy clustering. A modified version of fuzzy C-means (FCM) clustering, conditional FCM, is extended to incorporate a priori geometrical information from the spatial domain in order to improve image segmentation. This leads to a new algorithm (GGC-FCM) where the cluster guidance is determined by the membership values of neighbouring pixels. GGC-FCM is tested on synthetic and real images to demonstrate the improved image segmentation compared to traditional FCM. Copyright © 2002 John Wiley & Sons, Ltd.
this paper. The method is based on the segmentation of each color plane independently using a watershed based thresholding of the plane histograms. The segmentation maps obtained for each color plane are fused together according to a fusion operator taking into account a concordance of the labels of each segmentation map. This operator produces a fused segmentation map containing labeled and unlabeled pixels which is used as an image of seeds for a region growing method : the color watershed. The color watershed produces the final segmentation of the initial image. This segmentation scheme is experimented using several types of medical images and results in a fast and robust segmentation
We propose a color-image segmentation algorithm by unsupervised classification of pixels. The originality of the proposed approach consists in iteratively identifying pixel classes by taking into account both the pixel color distributions in several color spaces and their spatial arrangement in the image. In order to overcome the difficult problem of the color space choice, the algorithm selects the color space that is well suited to construct the class at each iteration step. The selection criterion is based on connectedness and color homogeneity measures of pixel subsets. In order to tune the sensitivity of segmentation, we introduce a hierarchical criterion that allows us to segment images with different numbers of regions as human observers do. Experiments carried out on the well-known Berkeley segmentation dataset show that this multicolor space approach succeeds in constructing classes that effectively correspond to regions in the image.
Résumé : L'utilisation de l'imagerie dans le domaine bio-végétal permet de réaliser des mesures quantitatives sans contact, automatisées, potentiellement à haut débit, et avec précision. Les systèmes d'imagerie 3D offrent la possibilité de caractériser la forme des végétaux. Jusqu'à présent, ces systèmes représentaient des coûts relativement importants. Depuis peu, des imageurs de profondeur bas-coût ont fait leur apparition. Dans ce mémoire, nous développons différentes études démontrant les potentialités d'un de ces imageurs de profondeur, pour des mesures scientifiques à différentes échelles du végétal. Nous décrivons des choix innovants permettant de contrôler la complexité des acquisitions et des traitements résultants.
Pour les plantes mono-axiales, nous utilisons une unique image de profondeur acquise en vue de dessus. Dans cette image, nous isolons chacune des feuilles avec une méthode originale de segmentation. Nous extrayons alors des informations quantitatives à partir de l'imageur de profondeur seul ou de son couplage avec une autre modalité d'imagerie. Pour les plantes complexes, nous décrivons l'ensemble du feuillage à partir d'images latérales délivrées par un imageur de profondeur motorisé. Cette description est réalisée par le traitement conjoint de l'ensemble des images via l'implémentation de quatre nouveaux descripteurs sur chacune d'elles. Pour les scènes forestières, nous montrons les capacités de méthodes de caractérisation fractale pour réaliser une description quantitative de ces scènes. Également, nous démontrons que des propriétés fractales sont présentes aussi bien dans les images de luminance que dans les images de profondeur de ces scènes naturelles.
Presented paper describes vision-based algorithm for 2D Rubik's cube state detection suitable for cases in which long-term fixed camera-cube position is not possible. The main focus was to provide a robust algorithm for position and color detection in order to overcome problems observed in previous version. First part of paper describes Hough transform and advanced clustering functions that were used for cube position detection. Described algorithm provides robustness to strong occlusions and various lighting conditions. Second part of paper describes color detection algorithm and problems of prior classification in various color spaces.
This paper proposes a novel technique to segment the color images combining M-Band Wavelet transform(MBWT) and Expectation Maximization (EM) with cost spatial refinement algorithm. One of the drawbacks of standard wavelets is that they are not suitable for the analysis of high frequency signals with relatively narrow bandwidth. This drawback has been overcome using MBWT. Also M-band wavelet decomposition yields a large number of sub bands which is required for improving the performance accuracy. The proposed algorithm first decomposes the input image into sixteen subimages by applying MBWT. Then, median feature is computed for each subimage and maximum energy subimage is chosen as the appropriate feature space on which EM with cost spatial refinement algorithm is applied. This new combined algorithm produces very good segmentation results by taking advantage of M-Band Wavelet feature extraction and EM with cost spatial refinement algorithm. The segmentation result is more homogeneous and quite consistent with the visualized color distribution in the objects of the original images compared to Fuzzy C means and K means spatial refinement algorithms. Also EM with cost spatial refinement algorithm needs less computational time compared to other clustering algorithms.
We present a new color image segmentation algorithm which is based on fuzzy mathematical morphology. After a color pixel projection into an attribute space, segmentation consists of detecting the different modes associated with homogeneous regions. In order to detect these modes, we show how a color image can be viewed as a fuzzy set with its associated membership function corresponding to a mode which is defined by a color cooccurrence matrix and by mode concavity properties. A new developed fuzzy morphological transformation is then applied to this membership function in order to identify the modes. The performance of our proposed fuzzy morphological approach is then presented using a test color image, and is then compared to the competitive learning algorithm.
Eye characteristics are significant information in pattern recognition. They are widely applied in many fields, such as human-computer interaction, face recognition and 3D face modeling from 2D images. Generally, the eye information detection is Based on gray images. However, color images provide more information than gray images. According to different applications, choosing a suitable color space is very important. In this paper, several eye features are compared from the view point of different color spaces, such as RGB, HIS, HSV. And some experiments have been done in the three color spaces. The extraordinary bright area of pupil in the H channel of HSV color space is confirmed. Moreover, pupil center is detected and estimated using morphology processing method in H channel. The results show that eyes features are more obvious in the HSV space, and feature extraction is more convenient. Furthermore, the experimental analysis can provide reference for future research on eye characteristic recognition.
Color space dimensionality possesses main problem in fast processing of color images so appropriate sampling of color images is very important. Unlike the existing statistical sampling algorithm, in this paper, a biologically inspired non-linear color image sampling technique has been proposed using non-uniform quantization of RGB space. Response of human retinal receptors to various light intensities is non-linear in nature. Buschbaum has qualitatively presented the non-linear tan-sigmoid model of the human vision as against the logarithmic and power law models. An experiment has been carried out on certified normal color vision observers in broad day light conditions to model their color vision. Readings of this experiment were used to compute the parameters of Red, Green and Blue color vision non-linearity presented by Buchsbaum. These parametric non-linearity equations were used to sample the color images and other applications of the work have been proposed. The non-linearity equations with respective parameters represent the models of Red, Green and Blue color vision receptors. Physiological limitations and facts of human vision have been utilized to compute the parameter.
In this paper we introduce a lattice algebra clustering technique for
segmenting digital images in the Red-Green- Blue (RGB) color space. The
proposed technique is a two step procedure. Given an input color image,
the first step determines the finite set of its extreme pixel vectors
within the color cube by means of the scaled min-W and max-M lattice
auto-associative memory matrices, including the minimum and maximum
vector bounds. In the second step, maximal rectangular boxes enclosing
each extreme color pixel are found using the Chebychev distance between
color pixels; afterwards, clustering is performed by assigning each
image pixel to its corresponding maximal box. The two steps in our
proposed method are completely unsupervised or autonomous. Illustrative
examples are provided to demonstrate the color segmentation results
including a brief numerical comparison with two other non-maximal
variations of the same clustering technique.
Based on the intelligent lighting control system required for the image processing tasks, in view of the Interior illuminance distribution uniform objective of the gray-scale difference of the status quo, using image processing techniques to intelligent lighting control system, proposed for the method to evaluate an average illumination for detection, coordinate mapping method of determine the students' positions, using fuzzy look-up table method. In view of the lack of traditional fixed threshold segmentation algorithm and traditional genetic segmentation algorithm, this paper proposes to establish dynamic multi-threshold template segment algorithm. Experiment proved, image segmentation algorithm proposed by this paper is more reliable, better real-timeness, Stronger applicable, so it has a good practical value.
A novel method of image segmentation was proposed in this paper to realize robustness and quickness in object recognition under varying illuminations. This method uses a seven-color flower (SCF) model based on a complete RGB space to realize dynamic tracking of the clustering parameters. The experiments of image segmentation under varying illuminations indicate that this model can not only make color segmentation real-time and robust but also meet the requirement of object recognition for autonomous mobile robot without prior environmental knowledge.
A new application of scale-space filtering to the classical problem of estimating the parameters of a normal mixture distribution is described. The technique involves generating a multiscale description of a histogram by convolving it with a series of Gaussians of gradually increasing width (standard deviation), and marking the location and direction of the sign change of zero-crossings in the second derivative. The resulting description, or fingerprint, is interpreted by relating pairs of zero-crossings to modes in the histogram where each mode or component is modeled by a normal distribution. Zero-crossings provide information from which estimates of the mixture parameters are computed. These initial estimates are subsequently refined using an iterative maximum likelihood estimation technique. Varying the scale or resolution of the analysis allows the number of components used in approximating the histogram to be controlled.
In this paper we present some extensions to the k-means algorithm for vector quantization that permit its efficient use in image segmentation and pattern classification tasks. It is shown that by introducing state variables that correspond to certain statistics of the dynamic behavior of the algorithm, it is possible to find the representative centers of the lower dimensional manifolds that define the boundaries between classes, for clouds of multi-dimensional, multi-class data; this permits one, for example, to find class boundaries directly from sparse data (e.g., in image segmentation tasks) or to efficiently place centers for pattern classification (e.g., with local Gaussian classifiers). The same state variables can be used to define algorithms for determining adaptively the optimal number of centers for clouds of data with space-varying density. Some examples of the application of these extensions are also given. Copyright c fl Massachusetts Institute of Technology, 19...
The segmentation of images should generate segments which correspond to objects, parts of objects, or groups of objects which appear in the image. This paper presents a description of a general segmentation method which can be applied to many different types of scenes. It describes the segmentation method in detail and discusses the potential performance of other segmentation techniques on general scenes. Also presented is a subset of the images which have been analyzed using this technique and a summary of the computational effort required. Details of some of the major programs are given in the appendix.
In this paper, a segmentation algorithm for color images based on the thresholding and the fuzzy c-means (FCM) techniques is presented. The scale-space filter is used as a tool for analyzing the histograms of three color components. The methodology uses a coarse-fine concept to reduce the computational burden required for the FCM. The coarse segmentation attempts to segment coarsely using the thresholding technique, while the fine segmentation assigns the pixels, which remain unclassified after the coarse segmentation, to the closest class using the FCM. Attempts also have been made to compare the performance of the proposed algorithm with other existing algorithms—Ohlander's, Rosenfeld's, and Bezdek's. Intensive computer simulation has been performed and the results are discussed in this paper. The simulation results indicate that the proposed algorithm yields the most accurate segmented image on the color coordinate proposed by Ohta et al., while requiring a reasonable amount of computational effort.
A new hybrid method is presented that combines the scale space filter (SSF) and Markov random field (MRF) for color image segmentation. The fundamental idea of the SSF is to use the convolution of Gaussian functions and image-histogram to generate a scale space image and then find the proper interval bounded by the local extrema of the derivatives. The Gaussian function is with zero mean and varied standard deviation. Using the SSF the different scaled histogram is separated into intervals corresponding to peaks and valleys. The MRF makes use of the property that each pixel in an image has some relationship with other pixels. The basic construction of an MRF is a joint probability given the original data. The original data is the image that is obtained from the source and the result is called the label image. Because the MRF needs a number of segments before it converges to the global minimum, the SSF is exploited to do coarse segmentation (CS) and then MRF is used to do fine segmentation (FS) of the images. Basically, the former is histogram-based segmentation, whereas the latter is neighborhood-based segmentation. Finally, experimental results obtained from using SSF alone, MRF using iterated conditional mode (ICM), and MRF using Gibbs sampling are compared.
When analyzing color pictures one often requires that the image be segmented into meaningful regions based upon the color characteristics of the scene. Such a problem can assume two different forms. The first variation arises when particular color space characteristics are known and the goal is to detect and extract image regions which possess the given color characteristics. The second case arises when there is no a priori knowledge about the color space characteristics of the scene and the goal is to segment the scene into meaningful regions which possess uniform color space characteristics. This paper describes an interactive system which uses a decision surface modeling approach to solve the first case and uses clustering techniques in the three-dimensional color space to solve the second case. A set of examples is presented and the performance of the system is evaluated.
In color image processing various kinds of color features can be calculated from the tristimuli R, G, and B. We attempt to derive a set of effective color features by systematic experiments of region segmentation. An Ohlander-type segmentation algorithm by recursive thresholding is employed as a tool for the experiment. At each step of segmenting a region, new color features are calculated for the pixels in that region by the Karhunen Loeve transformation of R, G, and B data. By analyzing more than 100 color features which are thus obtained during segmenting eight kinds of color pictures, we have found that a set of color features, , and , are effective. These three features are significant in this order and in many cases a good segmentation can be achieved by using only the first two. The effectiveness of our color feature set is discussed by a comparative study with various other sets of color features which are commonly used in image analysis. The comparison is performed in terms of both the quality of segmentation results and the calculation involved in transforming data of R, G, and B to other forms.
Many image segmentation techniques are available in the literature. Some of these techniques use only the gray level histogram, some use spatial details while others use fuzzy set theoretic approaches. Most of these techniques are not suitable for noisy environments. Some works have been done using the Markov Random Field (MRF) model which is robust to noise, but is computationally involved. Neural network architectures which help to get the output in real time because of their parallel processing ability, have also been used for segmentation and they work fine even when the noise level is very high. The literature on color image segmentation is not that rich as it is for gray tone images. This paper critically reviews and summarizes some of these techniques. Attempts have been made to cover both fuzzy and non-fuzzy techniques including color image segmentation and neural network based approaches. Adequate attention is paid to segmentation of range images and magnetic resonance images. It also addresses the issue of quantitative evaluation of segmentation results.
This paperr describes a clustering algorithm for segmenting the color images of natural scenes. The proposed method operates in the 1976 CIE (L∗, a∗, b∗)-uniform color coordinate system. It detects image clusters in some circular-cylindrical decision elements of the color space. This estimates the clusters' color distributions without imposing any constraints on their forms. Surfaces of the decision elements are formed with constant lightness and constant chromaticity loci. Each surface is obtained using only 1D histogramsof the L∗, H°, C∗ cylindrical coordinates of the image data or the extracted feature vector. The Fisher linear discriminant method is then used to project simultaneously the detected color clusters onto a line for 1D thresholding. This permits utilization of all the color properties for segmentation and inherently recognizes their respective cross correlation. In this respect, the proposed algorithm also differs from the multiple histogram-based thresholding schemes.
For the past decade, many image segmentation techniques have been proposed. These segmentation techniques can be categorized into three classes, (1) characteristic feature thresholding or clustering, (2) edge detection, and (3) region extraction. This survey summarizes some of these techniques. In the area of biomedical image segmentation, most proposed techniques fall into the categories of characteristic feature thresholding or clustering and edge detection.
Image segmentation is the process by which an original image is partitioned into some homogeneous regions. In this paper, a novel multiresolution color image segmentation (MCIS) algorithm which uses Markov random fields (MRF's) is proposed. The proposed approach is a relaxation process that converges to the MAP (maximum a posteriori) estimate of the segmentation. The quadtree structure is used to implement the multiresolution framework, and the simulated annealing technique is employed to control the splitting and merging of nodes so as to minimize an energy function and therefore, maximize the MAP estimate. The multiresolution scheme enables the use of different dissimilarity measures at different resolution levels. Consequently, the proposed algorithm is noise resistant. Since the global clustering information of the image is required in the proposed approach, the scale space filter (SSF) is employed as the first step. The multiresolution approach is used to refine the segmentation. Experimental results of both the synthesized and real images are very encouraging. In order to evaluate experimental results of both synthesized images and real images quantitatively, a new evaluation criterion is proposed and developed
A low-level segmentation methodology based upon fuzzy clustering principles is developed. The approach utilizes region growing concepts and a pyramid data structure for the hierarchical analysis of aerial images. It is assumed that measurement vectors corresponding to perceptually homogeneous regions cluster together in the measurement space. The fuzzy c-means (FCM) clustering algorithm is used in the formulation. Utilization of the fuzzy partitioning allows one to derive a correspondence between the cluster membership function values and (the proportions of) the classes constituting a region. Thus cluster membership values can be used to split mixture regions into smaller regions at a higher resolution level. The feasibility of the methodology is evaluated using a three-channel Landsat image. The results show that the FCM clustering can be used in the single-level segmentation; and that cluster membership function values derived using this algorithm can be utilized effectively as indicators of region homogeneity.
Vector quantization is intrinsically superior to predictive coding, transform coding, and other suboptimal and {em ad hoc} procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded. The key limitation of existing techniques is the very large randomly generated code books which must be stored, and the computational complexity of the associated encoding procedures. The quantization operation is decomposed into its rudimentary structural components. This leads to a simple and elegant approach to derive analytical properties of optimal quantizers. Some useful properties of quantizers and algorithmic approaches are given, which are relevant to the complexity of both storage and processing in the encoding operation. Highly disordered quantizers, which have been designed using a clustering algorithm, are considered. Finally, lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices. The code vectors are algorithmically generated in a simple manner rather than stored in a code book, and fast algorithms perform the encoding algorithm with negligible complexity.
In this paper, we present an approach to color image understanding that can be used to segment and analyze surfaces with color variations due to highlights and shading. The work is based on a theory - the Dichromatic Reflection Model - which describes the color of the reflected light as a mixture of light from surface reflection (highlights) and body reflection (object color). In the past, we have shown how the dichromatic theory can be used to separate a color image into two intrinsic reflection images: an image of just the highlights, and the original image with the highlights removed. At that time, the algorithm could only be applied to hand-segmented images. This paper shows how the same reflection model can be used to include color image segmentation into the image analysis. The result is a color image understanding system, capable of generating physical descriptions of the reflection processes occurring in the scene. Such descriptions include the intrinsic reflection images, an image segmentation, and symbolic information about the object and highlight colors. This line of research can lead to physicsbased image understanding methods that are both more reliable and more useful than traditional methods.
One of the key tools in applying physics-based models to machine vision has been the analysis of color histograms. In the mid-1980s it was recognized that the color histogram for a single inhomogeneous surface with highlights will have a planar distribution in color space. It has since been shown that the colors do not fall randomly in a plane, but form clusters at specific points. The shape of the histogram is related not only to the illumination color and object color, but also to such non-color properties as surface roughness and imaging geometry. We present here an algorithm for analyzing color histograms that yields estimates of surface roughness, phase angle between the camera and light source, and illumination intensity. These three scene parameters are related to three histogram measurements. However the relationship is complex and cannot be solved analytically. Therefore we have developed a method for estimating these properties by interpolating between histograms that come f...
Color information for region segmentation, Comput. »ision Graphics Image Process
- Yu-Ichi Ohta
- Takeo Kanade
- Toshiyuki Sakai
Yu-Ichi Ohta, Takeo Kanade and Toshiyuki Sakai, Color information for region segmentation, Comput. »ision Graphics Image Process. 13, 224—241 (1980).
Color image segmentation based on the 3D clustering and mor-phological operators
- S H Park
- I D Yun
- S U Lee
S. H. Park, I. D. Yun and S. U. Lee, Color image segmentation based on the 3D clustering and mor-phological operators, 2nd Asian Conf. on Comput. »ision, Vol.-III. pp. 253—257. Singapore, December 1995.
- R M Haralick
- L G Shapiro
R. M. Haralick and L. G. Shapiro, Computer and Robot
»ision: Vol. I, II. Addison-Wesley Reading, Massachusetts (1993).