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Image Analysis And Compact Coding By Oriented 2D Gabor Primitives
Abstract
Any effort to develop efficient schemes for image representation must begin by pondering the nature of image structure and image information. The fundamental insight which makes compact coding possible is that the statistical complexity of images does not correspond to their resolution (number of resolvable states) if they contain nonrandom structure, coherence, or local auto-correlation. These are respects in which real images differ from random noise: they are optical projections of 3-D objects whose physical constitution and material unity ensure locally homogeneous image structure, whether such local correlations are as simple as luminance value, or a more subtle textural signature captured by some higher-order statistic. Except in the case of synthetic white noise, it is not true that each pixel in an image is statistically independent from its neighbors and from every other pixel; yet that is the default assumption in the standard image representations employed in video transmission channels or the data structures of storage devices. This statistical fact - that the entropy of the channel vastly exceeds the entropy of the signal - has long been recognized, but it has proven difficult to reduce channel bandwidth without loss of resolution. In practical terms, the consequence is that the video data rates (typically 8 bits for each one of several hundred thousand pixels in an image mosaic, resulting in information bandwidths in the tens of millions of bits per second) are far more costly informationally than they need to be, and moreover, no image structure more complex than a single pixel at a time is explicitly extracted or encoded.
... Other models such as Fourier transformation have also been investigated (Bajcsy 1973; Julesz and Caelli 1979). The model presented here is based on Gabor filters (Gabor 1946; Turner 1986; Caelli and Moraglia 1985; Daugman 1987; Beck et al. 1987). The class of Gabor functions was described by Gabor (1946) and was extended to two dimensions by Daugman (1980 Daugman ( , 1987). ...
... The model presented here is based on Gabor filters (Gabor 1946; Turner 1986; Caelli and Moraglia 1985; Daugman 1987; Beck et al. 1987). The class of Gabor functions was described by Gabor (1946) and was extended to two dimensions by Daugman (1980 Daugman ( , 1987). Daugman showed that Gabor filters are optimal in the sense that they minimize the product of effective areas occupied in the 2-D space and 2-D frequency domains. ...
... The failure of the Gabor filter based model to predict terminator based discrimination is interesting in itself. Models based on linear filters are quiteDaugman 1987; Watson 1983; Wilson 1983), while above threshold some nonlinearities have to be postulated (Julesz 1980; Hochstein 1983, 1985). The general validity of the linear filter based model is also supported by electrophysiological studies reflecting properties of single cortical cells (Mareelja 1980; Daugman 1980). ...
The present paper presents a model for texture discrimination based on Gabor functions. In this model the Gabor power spectrum of the micropatterns corresponding to different textures is calculated. A function that measures the difference between the spectrum of two micropatterns is introduced and its values are correlated with human performance in preattentive detection tasks. In addition, a two stage algorithm for texture segregation is presented. In the first stage the input image is transformed via Gabor filters into a representation image that allows discrimination between features by means of intensity differences. In the second stage the borders between areas of different textures are found using a Laplacian of Gaussian operator. This algorithm is sensitive to energy differences, rotation and spatial frequency and is insensitive to local translation. The model was tested by means of several simulations and was found to be in good correlation with known psychophysical characteristics as texton based texture segregation and micropattern density sensitivity. However, this simple model fails to predict human performance in discrimination tasks based on differences in the density of terminators. In this case human performance is better than expected.
... Gabor filters [128][129][130][131][132] are a family of linear, frequency, and orientation-selective filters. They have been chosen for texture analysis applications due to the evidence from psychophysical research which indicated that the human brain performs a frequency analysis of images [133][134][135]. ...
... They have been chosen for texture analysis applications due to the evidence from psychophysical research which indicated that the human brain performs a frequency analysis of images [133][134][135]. The class of Gabor functions was first introduced by Gabor [132] and was extended to two dimensions by Daugman [131,136]. Daugman showed that Gabor filters are optimal in a way that they minimize the product of effective areas occupied in the 2D space and frequency domains. These filters can be described in terms of a sinusoidal plane wave of some spatial frequency and orientation within a two-dimensional Gaussian envelope. ...
Speckle has been widely considered a noisy feature in ultrasound images, thus it is intended to be suppressed and eliminated. On the other hand, speckle can be studied as a signal modeled by various statistical distributions or by analyzing its intensity with spatial relations in image space that characterize its nature, and hence, the nature of the underlying tissue. This knowledge can then be used in order to classify the different speckle regions into anatomical structures. In fact, speckle characterization in echocardiography and other ultrasonic images is important for motion tracking, tissue characterization, image segmentation, registration, and other medical applications for diagnosis, therapy planning and decision making. In this paper, we review and discuss various speckle characterization methods, which are often applied to confirm the speckle nature of the elements.
... Parametric adaptive time-frequency representations based on Gabor atoms [16] are possible, since the spectrogram, that is, the windowed Fourier transform module (absolute value), can be a part of the analysis toolkit using Gabor atoms (if we do not touch upon the newest and more sophisticated in positioning methods of representation of cyber-physical signatures with Gabor atoms [17]). Gabor atoms and Gabor atom network are used for modulation feature extraction of radar emitter signals and radar target recognition [18][19][20], as well as in the analysis of biomedical signals (for example, in EEG to detect seizures [21][22][23]). Note that in 1946 Dennis Gabor proposed the representation of signals in the form of linear combinations of "atoms", which later received his name. ...
Buryanskaya, E. L., Gradov, O. V., Gradova, M. A., Iordanskii, A. L., Maklakova, I. A., and Olkhov, A. A. (2024). Visualization and quantitative estimation of ferroelectric polymer fiber motility in time-resolved SEM using Gabor atoms. In: Advances in Transdisciplinary Engineering, volume 61, pages 689–696, IOS Press. http://dx.doi.org/10.3233/atde240821. The following brief communication discusses the possibility of applying time-resolved scanning electron microscopy methods (including Stroboscopic Scanning Electron Microscopy, Environmental Scanning Electron Microscopy, and Atmospheric Scanning Electron Microscopy) with correlation-spectral analysis in real-time for in situ measuring the mobility and mechanical properties of ferroelectric microfibers in an electric field and under the influence of ion particle beams in FIB-SEM technique or conventional electron beams in regular scanning electron microscopy. Extended periods of high temporal resolution monitoring lead to the necessity of expressing fiber mobility over time through some mathematical processing of the video stream, based on which reactivity, polarizability, conversion coefficients for piezoelectric effects in ferroelectric fibers, and dependencies of microelectromechanical dynamics on parameters of the interacting beam can be calculated. Physical “descriptors” are needed, i.e., compressed but heuristically valuable representations of time-resolved experimental data. We propose using wavelets or Gabor atoms for this purpose. The analysis is performed in real-time using the “QAVIS” software system developed by the Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, based on the FFTW library.
... The 2D Gabor function was originally introduced by [66] and since then it has been extensively used in the analysis of visual information [52,58,62]. In the context of the Fourier transform, the 2D Gabor function corresponds to the short-time Fourier function with a Gaussian window [52,53]: ...
We propose MomentsNeRF, a novel framework for one- and few-shot neural rendering that predicts a neural representation of a 3D scene using Orthogonal Moments. Our architecture offers a new transfer learning method to train on multi-scenes and incorporate a per-scene optimization using one or a few images at test time. Our approach is the first to successfully harness features extracted from Gabor and Zernike moments, seamlessly integrating them into the NeRF architecture. We show that MomentsNeRF performs better in synthesizing images with complex textures and shapes, achieving a significant noise reduction, artifact elimination, and completing the missing parts compared to the recent one- and few-shot neural rendering frameworks. Extensive experiments on the DTU and Shapenet datasets show that MomentsNeRF improves the state-of-the-art by {3.39\;dB\;PSNR}, 11.1% SSIM, 17.9% LPIPS, and 8.3% DISTS metrics. Moreover, it outperforms state-of-the-art performance for both novel view synthesis and single-image 3D view reconstruction. The source code is accessible at: https://amughrabi.github.io/momentsnerf/.
... The Gabor filter (Gabor, 1946;Daugman, 1987Daugman, , 1980, which was used for segmentation of the AFM images, is given by: gðx; y; l; u; c; s; gÞ ¼ exp À ...
Type III cadherin represents the ancestral form of classical cadherin in bilaterian metazoans. Drosophila possesses type III and type IVa cadherins, known as DN- and DE-cadherins, respectively. Mature DN- and DE-cadherins have 15 and 7 extracellular cadherin domain (EC) repeats, respectively, with DN-cadherin EC6–EC11 homologous to DE-cadherin EC1–EC6. These EC repeats contain predicted complete or partial Ca2+-free inter-EC linkers that potentially contribute to adhesion. Comparative structure–function studies of DN- and DE-cadherins may help us understand the ancestral and derived states of classical cadherin-mediated adhesion mechanisms. Here, using bead aggregation assays, we found that DN-cadherin EC1–EC11 and DE-cadherin EC1–EC6 exhibit Ca2+-dependent adhesive properties. Using high-speed atomic force microscopy (HS-AFM) imaging in solution, we show that both DN- and DE-cadherin ectodomains share a common morphological framework consisting of a strand-like and a globule-like portion. Furthermore, the DN-cadherin EC repeats are highly variable, flexible in morphology and have at least three bendable sites, one of which is located in EC6–EC11 and can act as a flexible hinge. Our findings provide insights into diversification of classical cadherin-mediated adhesion mechanisms.
This article has an associated First Person interview with the first author of the paper.
... Un filtre de Gabor est un filtre linéaire convolutif utilisant la décomposition fréquentielle pour analyser les propriétés texturales d'une image [Gabor, 1946] [Fogel et Sagi, 1989]. Ce filtre bidimensionnel minimise le produit des aires effectives occupées dans le domaine spatial et fréquentiel de l'image [Daugman, 1987]. En ce sens, les filtres de Gabor permettent une description compacte de l'espace image-fréquence. ...
L’histologie produit des images à l’échelle cellulaire grâce à des microscopes optiques très performants. La quantification du tissu marqué comme les neurones s’appuie de plus en plus sur des segmentations par apprentissage automatique. Cependant, l’apprentissage automatique nécessite une grande quantité d’informations intermédiaires, ou caractéristiques, extraites de la donnée brute multipliant d’autant la quantité de données à traiter. Ainsi, le nombre important de ces caractéristiques est un obstacle au traitement robuste et rapide de séries d’images histologiques. Les algorithmes de sélection de caractéristiques pourraient réduire la quantité d’informations nécessaires mais les ensembles de caractéristiques sélectionnés sont peu reproductibles. Nous proposons une méthodologie originale fonctionnant sur des infrastructures de calcul haute-performance (CHP) visant à sélectionner des petits ensembles de caractéristiques stables afin de permettre des segmentations rapides et robustes sur des images histologiques acquises à très haute-résolution. Cette sélection se déroule en deux étapes : la première à l’échelle des familles de caractéristiques. La deuxième est appliquée directement sur les caractéristiques issues de ces familles. Dans ce travail, nous avons obtenu des ensembles généralisables et stables pour deux marquages neuronaux différents. Ces ensembles permettent des réductions significatives des temps de traitement et de la mémoire vive utilisée. Cette méthodologie rendra possible des études histologiques exhaustives à haute-résolution sur des infrastructures CHP que ce soit en recherche préclinique et possiblement clinique.
... The 2D Gabor function was first proposed by Daugman [38], and since then, it has been widely used in the understanding of visual information. From the perspective of Fourier transform, the 2D Gabor function is the short-time Fourier function when the window function takes the gaussian window. ...
Object detection models based on convolutional neural networks (CNN) have achieved state-of-the-art performance by heavily rely on large-scale training samples. They are insufficient when used in specific applications, such as the detection of military objects, as in these instances, a large number of samples is hard to obtain. In order to solve this problem, this paper proposes the use of Gabor-CNN for object detection based on a small number of samples. First of all, a feature extraction convolution kernel library composed of multi-shape Gabor and color Gabor is constructed, and the optimal Gabor convolution kernel group is obtained by means of training and screening, which is convolved with the input image to obtain feature information of objects with strong auxiliary function. Then, the k-means clustering algorithm is adopted to construct several different sizes of anchor boxes, which improves the quality of the regional proposals. We call this regional proposal process the Gabor-assisted Region Proposal Network (Gabor-assisted RPN). Finally, the Deeply-Utilized Feature Pyramid Network (DU-FPN) method is proposed to strengthen the feature expression of objects in the image. A bottom-up and a top-down feature pyramid is constructed in ResNet-50 and feature information of objects is deeply utilized through the transverse connection and integration of features at various scales. Experimental results show that the method proposed in this paper achieves better results than the state-of-art contrast models on data sets with small samples in terms of accuracy and recall rate, and thus has a strong application prospect.
... At the earliest stages of visual processing, each neuron responds to stimulation in an isolated region of the visual field, termed classical receptive field (CRF) [1]. Elementary visual signals termed Gabor Patches (GPs) [2], match the CRF profiles in the primary visual cortex [2][3][4][5][6][7]. Response to GPs presented within the CRF of each neuron can be facilitated (i.e. ...
Collinear facilitation of contrast sensitivity supported by lateral interactions within primary visual cortex is implicated in contour and object perception, with neural correlates in several frequency bands. Although higher component of the ERP power spectrum, the gamma-band, is postulated to reflect object representation, attention and memory, its neuronal source has been questioned, suggesting it is an artifact reflecting saccadic eye movements. Here we explored the gamma-band activity during collinear facilitation with no saccade-related confounds. We used single-trial spectral analysis of ERP in occipital channels in a time-window of nearly complete saccadic suppression and discarded sporadic trials containing saccades, in order to avoid saccadic artifacts. Although converging evidence suggests that gamma-band oscillations emerge from local excitatory–inhibitory balance involving GABAergic inhibition, here we show activity amplification during facilitatory collinear interactions, presumably dominated by excitations, in the gamma-band 150–350 milliseconds following onset of low near-threshold contrast stimulus. This result highlights the potential role of gamma-band oscillations in neuronal encoding of basic processes in visual perception. Thus, our findings suggest that gamma-band ERP spectrum analysis may serve as a useful and reliable tool for exploring basic perception, both in normal adults and in special populations.
... La seconde école dominante, inspirée par l'équipe de Grossberg (Carpenter, Grossberg, & Mehanian, 1989;Gaussier, & Cocquerez, 1992;Grossberg, & Mingolla, 1985;Grossberg, & Todorovic, 1988;Grossberg, & Wyse, 1991), prône de débuter l'analyse par une détection des arêtes selon plusieurs directions pré-définies puis de choisir l'arête en chaque pixel selon l'orientation dominante détectée et selon l'orientation des arêtes dans le voisinage. Ces travaux s'inspirent largement de ce qui est connu du fonctionnement du cortex visuel chez les mammifères (Hubel, & Wiesel, 1959) (Carpenter, et al., 1989) (Daugman, 1987) qui modélise assez bien les cellules simples biologiques ou l'utilisation d'une cellule de Grossberg-Todorovic (Grossberg, et al., 1988) ...
... We have stressed that such filter-based methods lead to a passband-specific demodulation by each filter pair rather than to a complete and invertible image demodulation as in our proposed new transform. The currently popular energy models for texture segregation, 42 as originally proposed in 1983 by Caelli 43 using Fourier kernels to compute energy, are now typically based on this earlier idea 17,18 of taking the modulus of the output of local oriented quadrature 2D Gabor filters. Coding schemes based on these filters enjoy the advantage of maximizing their simultaneous resolution for both "what" and "where" information 7 because the underlying complex primitives minimize the conjoint 2D spatial/2D spectral uncertainty, 44 and they lead to decorrelated image representations 18 that therefore achieve large factors of entropy reduction. ...
We argue that some aspects of human spatial vision, particularly for textured patterns and scenes, can be described in terms of demodulation and predictive coding. Such nonlinear processes encode a pattern into local phasors that represent it completely as a modulation, in phase and amplitude, of a prediction associated with the image structure in some region by its predominant undulation(s). The demodulation representation of a pattern is an anisotropic, second-order form of predictive coding, and it offers a particularly efficient way to analyze and encode textures, as it identifies and exploits their underlying redundancies. In addition, self-consistent domains of redundancy in image structure provide a basis for image segmentation. We first provide an algorithm for computing the three elements of a complete demodulation transform of any image, and we illustrate such decompositions for both natural and synthetic images. We then present psychophysical evidence from spatial masking experiments, as well as illustrations of perceptual organization, that suggest a possible role for such underlying representations in human vision. In psychophysical experiments employing masks with more than two oriented Fourier components, we find that peaks of threshold elevation occur at locations in the Fourier plane remote from the orientations and frequencies of the actual mask components. Rather, as would occur from demodulation, these peaks in the frequency plane are related to the vector difference frequencies between the actual masking components and their spectral centers of mass. We offer a neural interpretation of demodulation coding, and finally we demonstrate a practical application of this process in a system for automatic visual recognition of personal identity by demodulation of a facial feature.
Military object detection technology plays an important role in realizing the informatization and intelligence of military equipment, but the complex environment and scarce sample data of military objects also become the difficulties of detection. This paper proposes a detection framework of military objects based on optimal Gabor filtering and deep feature pyramid networks. At first, we combine the texture characteristics of military objects with the requirements of detection tasks and proposed the Fine Region Proposal Network (FRPN). A set of Gabor filter is designed and screened in this scheme, we construct the optimal Gabor filter Banks by analyzing the image energy after Gabor transformation of some images in the dataset, shorting the time of feature extraction and reducing the amount of calculation. Then, the Renyi threshold segmentation method is adopted to obtain the region proposals. Finally, the Highly Utilized Feature Pyramid Networks (HU-FPN) is proposed to improve the detection effect of small objects. A bottom-up and a top-down feature pyramid is constructed in the stage. Through transverse connection and integration of features at various scales, the feature expression of small objects is enriched and the detection problem of small objects is effectively solved. The experimental results show that the method proposed in this paper has prominent advantages in accuracy, effectiveness and small object detection when compared with the state-of-the-art method, which can create good conditions for the realization of rapid and accurate detection of military objects and precise strike under military background.
Modern research in visual texture perception can be traced to the pioneering work of Julesz (1962), and Beck (1966). What exactly is visual texture? Even though visual texture is not easy to define, a good “stratified” definition was proposed by Gorea: “Visual texture is a 2D [two-dimensional] visual stimulus characterized by a visible grain. Visual grain consists of local modulations along dimensions such as luminance, color, and shape, which may or may not be discriminable. Two textures are visually different if they do not share the same grain and/or if they do not share, in the statistical sense, the same grain distribution across space.” (Gorea 1995, pp. 55–56). Figure 12.1 shows an example of texture-based segregation. In Fig. 12.1a, the central region consisting of X’s shows a marked segregation from the peripheral region composed of T’s. This is an example of pre-attentive or “pop-out” texture segmentation. However, in Fig. 12.1b, the central region comprising of L’s does not segregate preattentively from the peripheral regions composed of T’s.
It is well known that Fourier-phase is sufficient for image representation and reconstruction within a scale factor, under a variety of conditions. For a finite length sequence, i.e., a sampled signal, a finite number of Fourier coefficients suffices to reconstruct the sequence. Several algorithms exist for this purpose. A close form solution involves solving a large set of linear equations. Another approach is an iterative technique which involves repeated transformation between the frequency and the spatial domains. The application of these techniques to image reconstruction from global (Fourier) phase is, however rather limited in practice due to the computational complexity. In this paper we present a new approach to image representation by means of which, similarly to the biological processing at the level of the cortex, the partial information is defined by localized phase. Also, like processing in vision, dc is first extracted from the signal and signaled separately. Computational results and theoretical analysis indicate that image reconstruction from localized phase-only is more efficient than image reconstruction from global (Fourier) phase. It also lends itself to hardware implementation of fast algorithms using highly parallel architecture.
Texture is an important preattentive cue in region-based segmentation of images. In this paper, we provide an objective comparison of the properties of the Gabor functions and the circular- Mellin features for texture segmentation. The Gabor functions provide a spectral decomposition of a windowed image about a unique spatial frequency in the Cartesian coordinate system. The circular-Mellin operators represent the spectral decomposition of the image scene in the polar-log coordinate system and are invariant to both scale and orientation of the target. Coupled with the unique shift invariance property of the correlator architecture, these circular-Mellin operators can be used for rotation- and scale-invariant feature extraction. We note that while both these feature extractors have similar functional form, the distortion- invariant characteristics of the circular-Mellin operators make them preferable for texture segmentation. Segmentation results to demonstrate their salient properties are presented.
This paper presents a group theoretic approach to space frequency image analysis and synthesis. The Weil map-Zak transform provides a major tool for study certain nonabelian function theoretic concepts, which underly the Gabor expansion theory.
This project was an attempt to understand the major functions of early vision by considering how various components cooperate in preparing visual information to organize our perceptions of the world around us. To this end, and with the cooperation of SRI's Machine Vision Group, we assembled some of these functions in a computational working model, which can graphically display the spatial structure of the formation at a given stage of the visual process, in the form of a two-dimensional intensity array (or 'image'). This capability was developed to facilitate the study and comparison of retinal and cortical inputs and outputs of spatial information. The individual components of the model are well known, and the relations among them are based on available data from the literature. However, two aspects of this project seem novel. One is the exploitation of powerful, state-of-the-art tools of computational vision, such as Symbolics 3600-series LISP machines, to create and display our results. These tools were developed primarily for artificial intelligence purposes; they have rarely been used for basic studies in human vision. (JES)
The objective of this work is to develop automated techniques for recognizing the same objects in images that differ in scale, tilt, and rotation. Such perspective transformations of images are produced when aerial images of the same scene are taken from different vantage points. The algebraic methods developed previously do not utilize the intensity values of the images, i.e., their pixel gray levels. Since image features essential for object recognition, such as edges and local image textures, may be described in terms of derivatives and integrals of the image intensity, it is necessary to investigate whether certain differential and integral operators applied to different perspective views of the same object are also invariant under the perspective transformation. We proceed to derive new differential operators and their corresponding integral invariants for curves and planar objects. We introduce a variant form of Fourier expansion specially adapted to the projective transformation. Extensions to three dimensions are discussed, as well as applications to other image formation models such as synthetic aperture radar (SAR). These results are steps toward a computational model for perspective-independent object recognition.
Observers were shown patterns composed of two textures in which each texture contained two types of elements. The elements
were arranged in a striped pattern in the top and bottom regions and in a checked pattern in the center region. Observers
rated the degree to which the three regions were seen as distinct. When the elements were squares or lines, perceived segregation
resulting from differences in element size could be canceled by differences in element contrast. Minimal perceived segregation
occurred when the products of the area and the contrast (areal contrasts) of the elements were equal. This dependence of perceived
segregation on the areal contrasts of the elements is consistent with a simple model based on the hypothesis that the perceived
segregation of the regions is a function of their differential stimulation of spatial-frequency channels. Two aspects of the
data were not consistent with quantitative predictions of the model. First, as the size difference between the large and small
elements increased, the ratings at the point of minimum perceived segregation increased. Second, some effects of changing
the fundamental frequency of the textures were not predicted by the model. These discrepancies may be explained by a more
complex model in which a rectification or similar nonlinearity occurs between two stages of orientation- and spatial-frequency-selective
linear filters.
Texture is an important preattentive cue in region-based
segmentation of images. In this paper, we discuss the use of
circular-Mellin features for segmenting an image into homogenous
regions. The circular-Mellin operators represent the spectral
decomposition of the image scene in the polar-log coordinate system and
are invariant to both scale and orientation of the target. Coupled with
the unique shift invariance property of the correlator architecture,
these circular-Mellin operators can be used for rotation- and
scale-invariant feature extraction. We note that while both these
feature extractors have similar functional form to the Gabor functions,
the distortion-invariant characteristics of the circular-Mellin
operators make them preferable for texture segmentation. Segmentation
results to demonstrate their salient properties are presented
The virtual agile retina target acquisition and classification (VARTAC) system is a biologically inspired ATR system based upon a space-variant foveal rosette local spatial frequency measurement grid which saccades from one fixation point to another in an image to detect, center, false alarm filter, and classify targets. VARTAC crudely mimics mammalian saccadic eye movements to find “attractive” regions that may contain targets. Because of these features of the VARTAC design, the average computational burden per image for target acquisition and classification is significantly reduced in comparison with other contemporary ATR approaches. Further, because of the inherent power of the fovea! local spatial frequency-based methods used, on second-generation infrared images VARTAC exhibits a probability of target detection greater than 95%, and (on 10 target class plus clutter class problems) a probability of correct target classification greater than 90% and a probability of false alarm acceptance under 10%. Because of the fovea! local spatial frequency features and the rich training sets used, VARTAC is insensitive to target background, brightness, contrast level, contrast reversal, and geometry relative to the sensor (except that separately configured and trained VARTAC systems must be used for each of, typically, three or four overlapping range swaths covered by a sensor).
The authors present a novel approach to image representation using
partial information defined by the localized phase. The scheme is
implemented using the short-time (short-distance) Fourier transform.
This is a generalization of the Gabor scheme which is well-established
with regard to biological representation of visual information at the
level of the visual cortex. Similar to processing in vision, the DC
component is first extracted from the signal and treated separately.
Computational results and theoretical analysis indicate that image
reconstruction from the localized phase representation requires fewer
computer operations and yields an improved rate of convergence compared
to reconstruction from the global phase representation. It is also
implementable with fast algorithms using highly parallel architecture
Two new two dimensional (2-D) complex operators for estimating the energy and orientation of 2-D oriented patterns are proposed. The starting point for our work is a new 2-D extension of the Teager-Kaiser energy operator incorporating orientation estimation. The first new energy operator is based on partial derivatives and can be considered a local (point-based) estimator. Using a nonlocal (pseudo-differential) operator we derive a second and more general energy operator. A scale invariant nonlocal operator is derived from the recently proposed spiral phase quadrature (or Riesz) transform. The Teager-Kaiser energy operator and the phase congruency local energy are unified in a single equation for both 1-D and 2-D. Robust orientation estimation, important for isotropic demodulation of fringe patterns is demonstrated. Theoretical error analysis of the local operator is greatly simplified by a logarithmic formulation. Experimental results using the operators on noisy images are shown. In the presence of Gaussian additive noise both the local and nonlocal operators give improved performance when compared with a simple gradient based estimator.
Observers rated the degree of segregation between two textures, each composed of the same two element types but in differing arrangements (a checkerboard arrangement in the middle region of the pattern and a striped arrangement in the top and bottom regions). The two element types in a given pattern were either both solid squares or both center-surround elements. In center-surround elements the average luminance equaled the background luminance. The two elements types were identical in size but differed in sign and/or amount of contrast. Discrepancies between the observers' ratings of perceived segregation and the predictions of simple (linear) spatial-frequency and orientation channels models of texture segregation suggested adding nonlinear processes to the model. Complex channels (a rectification-type nonlinearity between two linear-filtering stages) can explain why some patterns made of center-surround elements segregate even though there is little energy at the spatial frequencies that differentiate the two textures. Complex channels cannot, however, explain the very poor segregation of "same-sign-of-contrast" patterns (where the luminances of the two element types were both far above or both far below the background). This second result might arise from a local nonlinearity preceding the channels and might be ascribed to retinal light adaptation except that it occurs at contrasts less than or equal to 25%! Alternatively, it might arise from normalization, which may result from intracortical inhibition. Some preliminary quantitative predictions were computed from two models, one incorporating complex channels and an early local nonlinearity, the other complex channels and normalization. With suitable choices of parameters, either model could account for the results.
This work presents evidence for a second stage of spatial filtering in early vision. This second stage operates on the output of the well known linear spatial filters and integrates their thresholded responses with a center-surround weighting function. The evidence for the existence of this second stage comes from experiments where observers have to detect a Gabor signal with known parameters (target) among a varied number of other Gabor signals having orthogonal orientation (distractors). Detection performance on this task depends on the number of distractors and the distance between them: when the number of distractors is small performance deteriorates with an increasing number of distractors; however, when the number of distractors becomes larger performance improves with an increasing number of distractors. This improvement depends on the spatial-frequency of the signals and their spatial separation. Best performance is achieved when the spatial separation between signals is larger than three times their center wavelength but smaller than nine times their wavelength, implying a second stage filtering with a center size of six wavelengths and a total size of 18 wavelengths. This second stage of filtering may underlie our ability to detect certain texture boundaries preatentively.
Five experiments investigated the perceived segregation of patterns composed of two types of squares arranged in vertical stripes in the top and bottom regions and in a checkerboard arrangement in the middle region. The squares were either equal in luminance and different in hue or equal in hue and different luminance. The results indicate that adapting to an achromatic luminance distant from the luminance of the squares increased the Weber threshold for discriminating luminance differences, but did not increase the Weber threshold for discriminating hue differences. The experiments also revealed that luminance is the primary factor affecting perceived segregation and that perceived brightness is secondary.
We extended perceptual studies of the Brodatz set of textured materials. In the experiments, texture perception for different texture sets, viewing distances, or lighting intensities was examined. Subjects compared one pair of textures at a time. The main task was to rapidly rate all of the texture pairs on a number scale for their overall dissimilarities first and then for their dissimilarities according to six specified attributes (e.g., texture contrast). The implied dimensionality of perceptual texture space was usually at least four, rather than three. All six attributes proved to be useful predictors of overall dissimilarity, especially coarseness and regularity. The novel attribute texture lightness, an assessment of mean surface reflectance, was important when viewing conditions were wide-ranging. We were impressed by the general validity of texture judgments across subject, texture set, and comfortable viewing distances or lighting intensities. The attributes are nonorthogonal directions in four-dimensional perceptual space and are probably not narrow linear axes. In a supplementary experiment, we studied a completely different task: identifying textures from a distance. The dimensionality for this more refined task is similar to that for rating judgments, so our findings may have general application.
A typical image processing neuro chip consists of a regular array of very simple cell circuits. When it is implemented by a CMOS process, two stability issues naturally arise. First, parasitic capacitors of MOS transistors induce temporal dynamics. Since a processed image is given as the stable limit point of the temporal dynamics, a temporally unstable chip is unusable. Second, because of the array structure, the node voltage distribution induces spatial dynamics, and it could behave in a wild manner, e.g. oscillatory. The main contributions are: (i) a clarification of the spatial stability issue; (ii) explicit if and only if conditions for the temporal and the spatial stability in terms of circuit parameters; (iii) a rigorous explanation of the fact that even though the spatial stability is stronger than the temporal stability, the set of parameter values for which the two stability issues disagree is of (Lebesgue) measure zero; and (iv) theoretical estimates of the processing speed.
It is noted that there are two stability issues in image
processing neuro chips: the temporal stability issue due to the
parasitic capacitors of an MOS process, and the spatial stability issue
due to the parallel array structure of chips. The authors present a
rigorous clarification of the spatial stability issue, and explicit `if'
and `only if' conditions for the temporal and the spatial stability.
Even though the spatial stability is stronger than the temporal
stability, the set of parameter values for which the two stability
issues disagree is of (Lebesgue) measure zero
The problem of signal approximation by partial sets of a given
nonorthogonal basis is addressed, motivated by the essentially practical
requirement of signal representation in infinite-dimensional spaces.
Utilizing the biorthonormal approach, a general theorem for optimal
vector approximation in Hilbert spaces is suggested, based on
distinction between two biorthonormal sets related to a partial basis. A
sufficient and necessary condition interrelating these sets is given,
and a general systematic method for deriving finite biorthonormal sets
is presented. This method uses an algebraic approach and thus obviates,
in the case of function spaces, the need for solving integral equations.
It is concluded that in cases of significant nonorthogonality, the
optimal approximation approach has greater accuracy and calculation
efficiency, from both the theoretical and numerical viewpoints
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