Conference PaperPDF Available

Scholar Model of Images, Objects and Superpixels in Questions and Answers



This paper presents a self-consistent mathematical model of a digital image, developed through laborious programming by trial and error. The model is described at the level of the problem statement, so that other models of the same type could be built in its likeness. The model class is defined by the elementary definitions of the basic concepts. Basic concepts are easily entered in the form of questions and formal definitions are introduced in the form of appropriate answers. Just in this paper the name "Scholar" of the model is introduced for the first time as a designation for models of such type.
Springer Nature 2021 L
X template
Scholar Model of Images, Objects and
Superpixels in Questions and Answers
Mikhail Kharinov1,1*
1*Laboratory of Big Data Technologies of Socio-Cyberphysical
Systems, St. Petersburg Federal Research Center of the Russian
Academy of Sciences (SPC RAS), 39, 14th Line V.O.,
St. Petersburg, 199178, Russia.
Corresponding author(s). E-mail(s): ;
This paper presents a self-consistent mathematical model of a digital
image, developed through laborious programming by trial and error.
The model is described at the level of the problem statement, so that
other models of the same type could be built in its likeness. The
model class is defined by the elementary definitions of the basic con-
cepts. Basic concepts are easily entered in the form of questions and
formal definitions are introduced in the form of appropriate answers.
Just in this paper the name “Scholar” of the model is intro-
duced for the first time as a designation for models of such type.
Keywords: Model, Image, Object, Superpixel, Definitions
1 Introduction
The emergence and overactive introduction of computers into our lives is
accompanied by a decrease in the activity of fundamental developments.
So, Computer Vision is overflowing with engineering developments designed
to automatically recognize images of a priori known content type. At the
same time, there is a lack of theoretical generalizations. And each practicing
researcher has to create his own heuvristic model of the image. Therefore, now
Springer Nature 2021 L
X template
2Scholar Model of Images, Objects and Superpixels
the most in demand are understandable models that are available to novice
researchers, regardless of what images the latter work with. This paper pro-
poses a mathematical model, which quite simply allows one to explain and
overcome the difficulties of detecting objects in a digital image.
2 Questionnaire of Image Model
The discussed model is called Scholar, since relies on the classical methods of
the approximation error Eminimization and is the simplest of the models that
provide clear answers to the questions listed in Tab. 1.
Table 1: Check questions on the mathematical model for detecting
objects in a digital image
No. Questions
1 What is missing when detecting objects in an image ?
2 What is the stumbling block when detecting objects ?
3 What are the input and output data for object detection ?
4 What is meant by an “ object ” ?
5 What does “ image ” mean ?
6 What are “ superpixels ”, i.e. image elements ?
7 What is the common and what is the difference between
objects, images and superpixels ?
8 What formal problem is posed and solved in the model ?
9 What method system is used ?
10 What tuning parameters arise in a model ?
11 What is the computational complexity ?
12 Does the model support reversible computations ?
13 Does the model assume network computing ?
14 What is preventing the implementation of the model ?
15 What is required to implement the model into the mass
practice of detecting objects ?
16 How can a model be tested with publicly available soft-
ware ?
Tab. 2provides answers to the questions of Tab. 1within the framework
of the Scholar model of image, superpixels and objects in the image.
Springer Nature 2021 L
X template
Scholar Model of Images, Objects and Superpixels 3
Table 2: Fundamentals of the Scholar model for detecting objects
in a digital image
No. Answers
1 In modern image processing, not enough attention is paid
to the calculation of actually optimal image approximations
with a minimum error Efor each number g= 1,2, . . . of
pixel clusters.
2 The optimal approximation in 2 colors is poorly approx-
imated by the clusters of pixels of the 3-color optimal
approximation of the image. For this and similar reasons,
there is an effect of overwriting the sharpest boundaries
between objects. And objects disappear.
3 Objects are detected directly in the original image. The
detection result is displayed as a grayscale image. It is
obtained by on-line multiple transformation by the thresh-
old ∂E
∂g of the binary hierarchy of suboptimal image
approximations to get the target object hierarchy ([1]).
4 An object means a union of “ base objects ” or a “ base
object ” part. Base object is a pixel cluster of the optimal
image approximation in the specified number of g0colors.
5Image is treated as a superposition of object hierarchies.
6Superpixels are defined as pixel clusters generated by inter-
secting of current number gof initial optimal image parti-
tions. Such superpixels provides the error-free constructing
of goptimal image partitions.
7 The image and objects are described by convex dependences
of the approximation errors Eon the cluster numbers g. In
contrast to the optimal image approximations, the approxi-
mations describing objects constitute a hierarchy, moreover,
a binary one. The sequence of approximations describing
superpixels is a hierarchy that is not binary and is described
by a non-convex dependence of the error Eon g.
8 Shcolar model poses and solves the problem of approaching
of a sequence of optimal image approximations by a binary
hierarchy of suboptimal image approximations.
9 The E-minimization is achieved by Ward’s recursive pixel
clustering by image parts in combination with Dvoenko’s
K-meanless method [2] and CI(Clustering Improvement)-
method of reversible splitting-and-merging of pixel clusters
10 At the moment the following parameters are provided:
1) the number of objects g0; 2) the number of superpixels
s; 3) the inhomogeneity parameter ∂E
∂g .
Continuation. . .
Springer Nature 2021 L
X template
4Scholar Model of Images, Objects and Superpixels
Table 2: (Continuation)
No. Answers
11 Computational complexity is much less than the quadratic
dependence on the number of pixels and tends to be almost
12 Algorithms for obtaining optimal approximations of a color
image in the mode of only merging or only splitting of pixel
clusters have not yet been found. So, the problem is solved
by the error Eminimizing in the process of high-speed
reversible computations.
13 All calculations in the model are performed in terms of the
Algebraic Multilayer Network (AMN) [1].
14 Experience has shown that computing in terms of AMN is
prohibitively difficult for ordinary programmers.
15 To implement the model in the mass practice of detecting
objects, it will be extremely useful to modernize the classic
clustering algorithms as part of MatLab or other similar
publicly available system software.
16 To test the model on the example of a grayscale image, one
can use Otsu’s multi-threshold and hierarchical methods.
3 Scholar Model Illustrated
To materialize the model as a working tool, it is appropriate to offer an
overview of [3], especially since there are some distortions of slides in the video.
The following illustrations relate to a simple mathematical Scholar model of a
digital image, in which it does not matter what is displayed. Any objects are
allowed in the image.
There have never been any previously generally accepted textbooks and
reference books on computer image processing. And now they are still not
there. Therefore, each researcher, as he gains experience, creates his own model,
as a rule, for a certain type of images. However, in the field of image processing,
it seems like the time has come for general mathematical models to emerge,
especially for object detection. If earlier only ready-made mathematical models
were tried on for the detection and recognition of objects, now it is enough to
choose the most suitable ones from the number of ready-made software and
algorithmic developments. For this, it would be good to organize an electronic
resource with a mandatory questionnaire for each mathematical model, where
the authors could, by filling out the questionnaire, upload materials according
to their models.
Any model contains definitions of concepts and algorithms. The main con-
cepts of Scholar model are: image, superpixels and objects, which are all made
up of pixels. These have structures and differ in structure. If in one or another
model it is impossible to formally distinguish between the concepts of an
Springer Nature 2021 L
X template
Scholar Model of Images, Objects and Superpixels 5
object, an image and a superpixel, then in such a model they are synonyms.
In our Scholar model images, objects, and superpixels are completely different
In our model the definitions mean the primary concepts from which the
algorithms follow. This is not the case in many other models. And, say, super-
pixels are defined as sets of pixels, calculated by a certain algorithm with
unproven convergence [4]–[6], which, of course, is not very good.
Compared to the other models [4]–[14] Scholar model defines superpixels
in the simplest way in accordance with Fig. 1.
Fig. 1 Superpixel definition scheme.
Fig. 1presents and illustrates the definition of superpixels. Above is a
formal definition, the meaning of which is to calculate the optimal image
approximations in 1, 2, 3, etc. colors and, then, to project on the plane of the
current partition of the boundaries between the pixel clusters of all previous
optimal image approximations. Fig. 1shows that by merging the clusters of the
current optimal partition it is impossible to get any of the previous partitions.
What gets in the way is the effect of the disappearance of the sharpest bound-
aries between the objects shown by dotted lines. In practice, this explains the
ineffectiveness of attempts to detect sharp edges by ”crawling” between the
image pixels. Global top-down processing is required.
Fig. 2illustrates the definition of superpixels in the same way as the pre-
vious one, but using a real Lena image as an example. The top row of pictures
shows the optimal approximations of the image. The bottom row of pictures
demonstrates the image partitioning into a nonlinearly growing number of
superpixels. The image in Fig. 2is gray, but can be colored. So far, hands have
not yet reached ”Lena” in color.
Springer Nature 2021 L
X template
6Scholar Model of Images, Objects and Superpixels
Fig. 2 The real hierarchy of superpixels.
Fig. 3shows the graphical characteristics of superpixels. On the left is the
number sof superpixels depending on the number gof colors in the optimal
image approximation. On the right is the standard deviation σdepending on
the number of colors.
The difference between the curves in both plots indicates that the sequence
of best approximations of the image is not hierarchical. The graph on the right
shows that the superpixel hierarchy is not convex. Moreover, it is not binary.
Fig. 3 Graphical description of superpixels and optimal approximations.
Fig. 4shows a table of the numerical characteristics of superpixels. Usually,
in the considered range of the cluster numbers, no one even tries to calculate
Springer Nature 2021 L
X template
Scholar Model of Images, Objects and Superpixels 7
all optimal approximations due to the supposedly excessive computational
complexity. However, this is not at all the case. Accounting that a very limited
class of input data (images) is considered, and it is not required to obtain an
exact solution to the optimization problem, the task is quite solvable.
gσs g σs g σs g σs
1 55,8832 1 16 3,92460 46 31 1,87573 79 46 1,29542 106
2 30,6456 2 17 3,70326 50 32 1,79485 79 47 1,26794 107
3 21,2174 4 18 3,50441 55 33 1,72854 80 48 1,23991 109
4 14,9645 7 19 3,32383 60 34 1,68547 82 49 1,21323 110
5 11,6976 11 20 3,15658 63 35 1,64729 84 50 1,18618 111
6 10,0398 16 21 3,0126 66 36 1,61313 87 51 1,16091 112
7 8,46072 18 22 2,87305 67 37 1,57894 89 52 1,13576 112
8 7,51121 24 23 2,73844 67 38 1,54589 90 53 1,11091 114
9 6,81359 27 24 2,60572 68 39 1,51218 92 54 1,08554 115
10 6,14397 30 25 2,49076 70 40 1,4785 94 55 1,06012 118
11 5,57864 33 26 2,37391 70 41 1,44586 96 56 1,03435 119
12 5,11403 36 27 2,25584 74 42 1,414 97 57 1,00904 120
13 4,75689 39 28 2,15389 76 43 1,38327 96 58 0,9852 123
14 4,42306 41 29 2,05655 78 44 1,3534 101 59 0,96397 124
15 4,17825 43 30 1,95565 79 45 1,32287 104 60 0,94304 126
Fig. 4 The number sof superpixels to reproduce of g= 1 60 optimal approximations for
Lena image with minimal standard deviation σ.
Fig. 5graphically illustrates Scholar model for object detection and allows
one to understand and distinguish between the formal concepts of images,
objects and superpixels.
In Scholar model, the problem of approaching a series of optimal image
approximations (gray curve) is posed and solved using a “convex” binary hier-
archy of suboptimal approximations, which contains an optimal approximation
with a given number g0of pixel clusters (bold black curve). The upper none-
convex curve describes the superpixel hierarchy. Due to the ambiguity of the
solution to the optimization problem, two main tuning parameters appear in
Scholar Model, namely: a) the number Aof optimal approximations repro-
duced without errors or the number S(A) of superpixels, and b) the number g0
of basic objects in the image. Basic objects are the clusters of a given optimal
approximation, unions or parts of which constitute objects and approach the
“objects of interest”. The objects form a binary hierarchy and are described
by a convex curve. An image is a non-hierarchical structure and is interpreted
as a superposition of object hierarchies described by the convex curves. Super-
pixels are the pixel clusters generated by the intersection of a series of optimal
approximations. Superpixels form a non-binary “non-convex” hierarchy.
Fig. 6lists main methods, which in Scholar model provide real minimization
of approximation error, i.e. total squared error.
To work with the optimal image approximations Scholar model provides a
system of three modernized methods of classical cluster analysis, namely:
1. Recursive Ward’s method of pixel clustering by image parts [15].
2. Reversible split-and-merge CI (Clustering Improvement) method [15].
3. Refined K-meanless method, that is, the K-means method, improved by
Sergey D. Dvoenko [2,16].
Springer Nature 2021 L
X template
8Scholar Model of Images, Objects and Superpixels
Fig. 5 Graphical description of objects in the image consisting of superpixels.
For active practical implementation of the model, it would be extremely useful
to develop and strengthen the original methods of classic cluster analysis,
which are available in MatLab, however, so far without the necessary tuning
It should be noted that for gray images of minimal sizes, instead of the
listed methods, it is permissible to use the multi-threshold and hierarchical
versions of Otsu method [1720].
Fig. 6 System of pixel clustering methods.
Springer Nature 2021 L
X template
Scholar Model of Images, Objects and Superpixels 9
All calculations in the model are reversible and are performed within
the framework of a special data structure. In terms this data structure an
equivalent computational version of the model is implemented (Fig. 7).
Fig. 7 Data structure starting point.
The mentioned data structure is a so-called Algebraic Multilayer Network
(AMN), which serves the sole purpose of speeding up calculations with pixel
sets as with individual pixels. AMN consists of Sleator-Tarjan dynamic trees
and cyclic graphs using for high-speed computing. AMN can be viewed as an
analogue of natural neural networks. At the same time, they are an alternative
to modern artificial neural networks (ANN). Specific algorithms have a long
history of routine computations [1]. In Russia, Sleator-Tarjan dynamic trees are
practically unused. But in Russia there is also no publicly available domestic
software such as MatLab, where AMN would be useful.
On the other hand, in Russia for several decades leading scientists have been
developing an algebraic model of a full cycle of image processing [21]. The
disadvantage of this model is that it does not formulate in an intelligible way
the exploitable key properties of the image. This entails a rather cumbersome
mathematical apparatus that must be mastered in order to appreciate the
merits of the model.
In Scholar model, the non-hierarchical nature of ordered image structure
is exploited as the main property of an image. The concepts of superpixels,
objects and images are fundamentally different from each other due to the
non-hierarchy of the latter. If the optimal approximations of an image are
hierarchical, then images, objects and superpixels do not differ at all in their
Springer Nature 2021 L
X template
10 Scholar Model of Images, Objects and Superpixels
structure. Therefore, in this case, these are synonymous. Assuming that the
image can be generated by the geometric combination of arbitrary objects
with different hierarchical structure, it is difficult to expect that the result of
such object combining will also posess a hierarchical structure. So, the basic
assumption of the Scholar model looks quite plausible.
In general, in the paper we gave a brief overview of Scholar model, in
defined the concepts of images, superpixels and objects;
illustrated the definitions using the example of standard Lena image;
listed the methods needed to actually minimize the total squared error of
piecewise constant image approximations;
mentioned the data structure for high-speed computations.
The main conclusion from the paper is that at present the theory of object
detection probably lags somewhat behind numerous engineering solutions for
images from specific subject areas. However, in the future, the development
of scientific generalizations is expected based on the modernization of algo-
rithms for real minimization of the approximation error (root-mean-square
error, MSE) in publicly available software such as MatLab and others.
This research was funded within the framework of the budgetary theme 0060-
2019-0011 (Fundamentals and technologies of big data for sociocyberphysical
[1] Kharinov M. V., Buslavsky A. N. Object Detection in Color Image //
14th International Conference on Pattern Recognition and Information
Processing (PRIP’2019), Minsk: Publishing Center of BSU, 43–47,2019.
[2] Dvoenko S. D. Meanless k-means as k-meanless clustering with the bipar-
tial approach // Proc. of the 12th Int. Conf. on Pattern Recognition and
Information Processing, 50–54, 2014.
[3] Kharinov M. V. Superpixel Clustering for Detection of Binary Object
Hierarchy Using Modernized Classical Clustering Methods // Pattern
Recognition and Information Processing (PRIP’2021) / Proceedings
of the 15th International Conference, Minsk: Publishing Center of
BSU, 198–201, 2021.
list=TLGGIpwO79c2W2swMzEwMjAyMQ — from 2:18 till 2:27.
[4] Comaniciu D. and Meer P. Mean Shift: A Robust Approach toward
Feature Space Analysis // IEEE Trans. Pattern Analysis and Machine
Intelligence, 24 (5), pp. 603–619, May 2002.
[5] Levinshtein A., Stere A., Kutulakos K. N., Fleet D. J., Dickinson S. J.
and Siddiqi K. Turbopixels: Fast superpixels using geometric flows, IEEE
transactions on pattern analysis and machine intelligence, 31(12), pp.
2290–2297, 2009.
Springer Nature 2021 L
X template
Scholar Model of Images, Objects and Superpixels 11
[6] Lv X., Wang S., Dai S., Xu X. and Nakamura A. Superpixel segmenta-
tion methods and systems, U.S. Patent 8,472,718, 2013.
[7] Wang M., Liu X., Gao Y., Ma X. and Soomro N. Q. Superpixel segmen-
tation: A benchmark // Signal Processing: Image Communication, 56,
28–39, 2017.
[8] Achanta R., Shaji A., Smith K., Lucchi A., Fua P. and S¨usstrunk S. SLIC
superpixels compared to state-of-the-art superpixel methods // IEEE
transactions on pattern analysis and machine intelligence 34(11), 2274–
2282, 2012.
[9] Baraldi A., Tiede D., Lang S. Automated Linear-Time Detection and
Quality Assessment of Superpixels in Uncalibrated True-or False-Color
RGB Images // arXiv preprint, arXiv: 1701.01940, 14 pp. 2017.
[10] Vargas-Mu˜noz J. E., Chowdhury A. S., Alexandre E. B., Galv˜ao F. L.,
Miranda P. A. V. and Falc˜ao A. X. An iterative spanning forest frame-
work for superpixel segmentation // IEEE Transactions on Image
Processing 28(7), 3477–3489, 2019.
[11] Zhu L. , Klein D. A., Frintrop S., Cao Z. , Cremers A. B. A Multi-size
Superpixel Approach for Salient Object Detection based on Multivari-
ate Normal Distribution Estimation // IEEE Transactions on Image
Processing 23(12), 5094–5107, 2014, doi:10.1109/TIP.2014.236102.
[12] Kaur S. and Bansal R. K. Comparative analysis of superpixel segmenta-
tion methods // International Journal of Engineering Technologies and
Management Research 5(3), 9 pp. 2018.
[13] Abdel-Hakim A. E., Izz M. and El-Saban M. Graph-based superpixel
labeling for enhancement of online video segmentation // 2013 IEEE
Second International Conference on Image Information Processing (ICIIP-
2013), IEEE, 101–106, 2013.
[14] Farag A., Lu L., Roth H. R., Liu J., Turkbey E. and Summers R. M. A
Bottom-Up Approach for Pancreas Segmentation Using Cascaded Super-
pixels and (Deep) Image Patch Labeling // IEEE Transactions on Image
Processing 26(1), 386–399, 2017. doi: 10.1109/tip.2016.2624198
[15] Khanykov I. G., Kharinov M. V., Patel C. Image Segmentation Improve-
ment by Reversible Segment Merging // in: 2017 International Conference
on Soft Computing and its Engineering Applications: Harnessing Soft
Computing Techniques for Smart and Better World, icSoftComp 2017.
Harnessing Soft Computing Techniques for Smart and Better World. 1–8,
[16] Kharinov M. V. Reclassification formula that provides to surpass
K–means method // arXiv preprint, arXiv: 1209.6204v1, 10 pp., 2012.
[17] Kharinov M. V. Pixel Clustering for Color Image Segmentation //
Programming and Computer Software, 41(5), 258–266, 2015, doi:
[18] Kharinov M. V. Model of the quasi-optimal hierarchical segmentation
of a color image // J. Opt. Technol. 82(7), 425–429, 2015, doi:
[19] Otsu N. A threshold selection method from gray-level histograms // IEEE
transactions on systems, man, and cybernetics, 9(1), 62–66, 1979.
Springer Nature 2021 L
X template
12 Scholar Model of Images, Objects and Superpixels
[20] Liao P. S. , Chen T. S. and Chung P. C. A fast algorithm for multilevel
thresholding // J. Inf. Sci. Eng., 17(5), 713–727, 2001.
[21] Gurevich I. B., Yashina V. V. Algebraic Interpretation of Image Analy-
sis Operations // Pattern Recognition and Image Analysis (Advances in
Mathematical Theory and Applications), 29 (3) 389–403, 2019.
ResearchGate has not been able to resolve any citations for this publication.
Conference Paper
Full-text available
In this paper the problem of automatized object detection in a color image is treated. The solution basing on the classic pixel clustering methods is developed. The parameter for the heterogeneity of image areas is introduced. The method for markup of an image with automatically produced object names is proposed. The data structure is described. The computational complexity of clustering algorithms is estimated.
Full-text available
Superpixel segmentation has become an important research problem in image processing. In this paper, we propose an Iterative Spanning Forest (ISF) framework, based on sequences of Image Foresting Transforms, where one can choose i) a seed sampling strategy, ii) a connectivity function, iii) an adjacency relation, and iv) a seed pixel recomputation procedure to generate improved sets of connected superpixels (supervoxels in 3D) per iteration. The superpixels in ISF structurally correspond to spanning trees rooted at those seeds. We present five ISF methods to illustrate different choices of its components. These methods are compared with approaches from the state-of-the-art in effectiveness and efficiency. The experiments involve 2D and 3D datasets with distinct characteristics, and a high level application, named sky image segmentation. The theoretical properties of ISF are demonstrated in the supplementary material and the results show that some of its methods are competitive with or superior to the best baselines in effectiveness and efficiency.
Full-text available
Image segmentation using a hierarchical sequence of piecewise constant approximations that minimally differ from the original image in terms of the total squared error is discussed. It is proposed to obtain these approximations by two combined clustering and segmentation methods based on clustering image pixels using Ward’s method. In the first method, the number of segments in clusters is reduced in the course of hierarchical clustering by reclassifying pixels from one cluster to another. In the second method, a limited number of superpixels representing connected segments of the image are formed by enlarging source pixels, and then the superpixels are clusterized by Ward’s method. To decompose the image into superpixels, the segmentation quality is improved while preserving the number of segments. As a result, a noticeable improvement in the quality of image approximations is achieved, and their invariant encoding gives a marking of the image for subsequent object detection.
Full-text available
This paper discusses the solution of the problem of segmenting a digital image by means of a hierarchical sequence of piecewise-constant approximations that minimally differ from the image in the rms deviation. Analytical justification is given for the computations at the stage of preliminary automatic processing of the image without using controlling parameters. An algorithm is presented for combined segmentation/quality-improvement/clusterization and is illustrated by examples. (C) 2015 Optical Society of America.
Full-text available
Robust automated organ segmentation is a prerequisite for computer-aided diagnosis (CAD), quantitative imaging analysis, detection of pathologies and surgical assistance. We present a fully-automated bottom-up approach for pancreas segmentation in abdominal computed tomography (CT) scans. The method is based on a hierarchical cascade of information propagation by classifying image patches at different resolutions and (segments) superpixels. There are four stages in the system: 1) decomposing CT slice images as a set of disjoint boundary-preserving superpixels; 2) computing pancreas class probability maps via dense patch labeling; 3) classifying superpixels by pooling both intensity and probability features to form empirical statistics in cascaded random forest frameworks; and 4) simple connectivity based post-processing. The dense image patch labeling is conducted by two schemes: efficient random forest classifier on image histogram, location and texture features; and more expensive (but with better specificity) deep convolutional neural network classification, on larger image windows (i.e., with more spatial contexts). Oversegmented 2D CT slices by the Simple Linear Iterative Clustering approach are adopted through model/parameter calibration and labeled at the superpixel level for positive (pancreas) or negative (non-pancreas background) classes. Evaluation of the approach is done on a database of 80 manually segmented CT volumes in six-fold cross-validation. Our achieved results are comparable, or better than the state-of-the-art methods (evaluated by leave-one-patient-out), with a Dice coefficient of 70.7% and Jaccard Index of 57.9%. In addition, the computational efficiency has been drastically improved in the order of 6~8 minutes, comparing with others of >=10 hours per testing case.
Superpixel segmentation showed to be a useful preprocessing step in many computer vision applications. Superpixel’s purpose is to reduce the redundancy in the image and increase efficiency from the point of view of the next processing task. This led to a variety of algorithms to compute superpixel segmentations, each with individual strengths and weaknesses. Many methods for the computation of superpixels were already presented. A drawback of most of these methods is their high computational complexity and hence high computational time consumption. K mean based SLIC method shows better performance as compare to other while evaluating on the bases of under segmentation error and boundary recall, etc parameters.
The study is devoted to mathematical and functional/physical interpretation of image analysis and processing operations used as sets of operations (ring elements) in descriptive image algebras (DIA) with one ring. The main result is the determination and characterization of interpretation domains of DIA operations: image algebras that make it possible to operate with both the main image models and main models of transformation procedures that ensure effective synthesis and realization of the basic procedures involved in the formal description, processing, analysis, and recognition of images. The applicability of DIAs in practice is determined by the realizability—the possibility of interpretation—of its operations. Since DIAs represent an algebraic language for the mathematical description of image processing, analysis, and understanding procedures using image transformation operations and their representations and models, the authors consider an algebraic interpretation. These procedures are formulated and implemented in the form of descriptive algorithmic schemes (DAS), which are correct expressions of the DIA language. The latter are constructed from the processing and transformation of images and other mathematical operations included in the corresponding DIA ring. The mathematical and functional properties of DIA operations are of considerable interest for optimizing procedures of processing and analyzing images and constructing specialized DAS libraries. Since not all mathematical operations have a direct physical equivalent, the construction of an efficient DAS for image analysis involves the problem of interpreting operations for DAS content. Research into this problem leads to the selection and study of interpretation domains of DIA operations. The proposed method for studying the interpretability of DIA operations is based on the establishment of correspondence between the content description of the operation function and its mathematical realization. The main types of interpretability are defined and examples given of the interpretability/uninterpretability of operations of a standard image algebra, which is a restriction of the DIA with one ring.
Conference Paper
In this paper, we propose a novel approach for video segmentation. The proposed work is based on exploiting a superpixel-based image segmentation approach to improve the performance of state-of-the-art foreground/background segmentation techniques. A fusion between a bilayer segmentation and a geodesic segmentation approaches with a graph-based superpixel segmentation method is performed. Four different combination alternatives are investigated in terms of performance and efficiency. Manually-labeled ground truth video sequences as well as our own recorded video sequences were used for evaluation purposes. The evaluation results confirm the potential of the proposed method in enhancing the accuracy of the video segmentation over the state-of-the-art.