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1

Regularising Ill-posed Discrete Optimisation: Quests with P Systems

Nicolescu R., Gimel’farb G., Morris J., Delmas P., Gong R.

Fundamenta Informaticae

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2014

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Vol. 131, nr 3-4

465--483

EN

We propose a novel approach to justify and guide regularisation of an ill-posed one-dimensional global optimisation with multiple solutions using a massively parallel (P system) model of the solution space. Classical optimisation assumes a well-posed problem with a stable unique solution. Most of important practical problems are ill posed due to an unstable or non-unique global optimum and are regularised to get a unique best-suited solution. Whilst regularisation theory exists largely for unstable unique solutions, its recommendations are often routinely applied to inverse optical problems with essentially non-unique solutions, e.g. computer stereo vision or image segmentation, typically formulated in terms of global energy minimisation. In these cases the recommended regularisation becomes purely heuristic and does not guarantee a unique solution. As a result, classical optimisation algorithms: dynamic programming (DP) and belief propagation (BP) – meet with difficulties. Our recent concurrent propagation (CP), leaning upon the P systems paradigm, extends DP and BP to always detect whether the problem is ill posed or not and store in the ill-posed case an entire space of solutions that yield the same global optimum. This suggests a radically new path to proper regularisation: select the best-suited unique solution by exploring statistical and structural features of this space. We propose a P systems based implementation of CP and set out as a case study an application of CP to the image matching problem in stereo vision.

2

Stereo matching and disparity calculation based on discrete orthogonal moments of Chebyshev, Legendre and Zernike

Andrysiak T.

Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

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2011

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z. 14

13-31

EN

In the article we present various theoretical and experimental approaches to the problem of stereo matching and disparity estimation. We propose to calculate stereo disparity in the moments space, but we also present numerical and correlation based methods. In order to calculate disparity vector we decided to use discrete orthogonal moments of Chebyshev, Legendre and Zernike. In our research of stereo disparity estimation all of these moments were tested and compared. Experimental results confirm effectiveness of the presented methods of determining stereo disparity and stereo matching for machine vision applications.

PL

W artykule przedstawiono teoretyczne i eksperymentalne podejścia do problemu pasowania i oceny niezgodności stereoskopowej. Zaproponowano realizacje obliczeń niezgodności stereoskopowej w przestrzeni momentów otrogonalnych, jak również przedstawiono podstawy do obliczeń numerycznych i metod opartych na korelacji. W celu obliczania wektora niezgodności zdecydowano się na użycie dyskretnych momentów ortogonalnych Chebysheva, Legendre'a i Zernike'a. W procesie badawczym oceny niezgodności stereoskopowej wszystkie proponowane momenty były testowane i porównywane. Wyniki badań potwierdzają skuteczność prezentowanych metod określania niezgodności i pasowania stereoskopowego dla zastosowań widzenia maszynowego.

3

Recursive techniques for fast stereovision with low quality images in mobile robotics

Klimaszewski J., Putz B.

Problemy Eksploatacji

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2008

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nr 4

91-99

EN

One of the main problems in mobile robotics is obtaining knowledge about the surroundings from sensor data. This article describes attempts of fast 3D observed scene feature extraction based on information from a two-camera stereovision system. The additional assumption is that the robot vision system, dedicated to the navigation purpose, should be able to work with low quality images. The power of recursive techniques in the implementation of real-time working algorithms is presented in regard to standard area-based stereo matching but mainly focused on the new recursive algorithm for characteristic object segmentation in low quality images.

PL

Artykuł opisuje próby ekstrakcji cech trójwymiarowych obserwowanej sceny na podstawie informacji, pochodzącej z dwukamerowego systemu stereowizyjnego robota mobilnego. Jako dodatkowe założenie przyjęto, że system wizyjny robota, przeznaczony do celów nawigacji, powinien działać bazując nawet na obrazach niskiej jakości, która często jest efektem braku sztywności układu kamer podczas ruchu robota. Tematem wiodącym jest ukazanie siły technik rekurencyjnych, pozwalających na implementację algorytmów pracujących w czasie rzeczywistym. Zaprezentowano zasadę stosowania rekurencji do eliminacji obliczeń Redundantnych w algorytmach stereoskopowego dopasowywania obszarami oraz nowy algorytm rekurencyjny opracowany w celu wychwytywania obiektów charakterrystycznych w obrazach niskiej jakości. Algorytm, po wykonanej filtracji LoG, pozwala na wykrywanie obiektów dużych oraz grup małych obiektów, zależnie od ustawionego progu. Ponadto, zastosowanie algorytmu nie wymaga użycia dodatkowych metod usuwania szumów z obrazu. Opracowana metoda, przeznaczona do przygotowania obrazów stereowizyjnych do dalszej analizy, pozwala zachować w postaci obiektów większą ilość charakterystycznych cech widocznych na obrazie. Wyodrębnione obiekty mają umożliwić dalszą rekonstrukcję sceny 3D.

4

Metoda poszukiwania strukturalnie niedokładnej odpowiedniości elementów obrazów poprzez poszukiwanie klik optymalnych

Bal A.

Pomiary Automatyka Kontrola

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2007

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R. 53, nr 5

9-11

PL

W pracy przedstawiono idee nowych, wykorzystujących informacje o strukturze obrazów, metod poszukiwania niedokładnej odpowiedniości elementów obrazów. W prezentowanych metodach poszukiwanie odpowiedniości elementów obrazów sprowadzono do zadania ustalenia niedokładnej odpowiedniości odpowiednio zdefiniowanych grafów. Na potrzeby rozwiązania tego zadnia opracowano metodę poszukiwania odpowiedniości grafów przez poszukiwanie klik optymalnych. Jako przykład zastosowania prezentowanych metod przedstawiono ich wykorzystanie w zadaniu poszukiwania stereokorespondencji.

EN

In this paper the ideas of novel methods for finding inexact correspondence of image elements, using structural information, are presented. Task of matching image elements is reduced to the problem of inexact graph matching in accordingly defined graphs. For solving this problem method of finding graph matching by optimal clique finding was developed. As an example of practical usage of the described methods, their application in problem of stereomatching is presented.

5

Dense depth map reconstruction by phase difference-based algorithm under influence of perspective distortion

El-Etriby S., Al-Hamadi A., Michaelis B.

Machine Graphics and Vision

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2006

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Vol. 15, No. 3/4

349-361

EN

This paper describes a novel phase difference-based algorithm applied to the corresponding points in two views, which takes into account the surface perspective distortion (foreshortening). The challenges arise from the fact that stereo images are acquired from slightly different views. Therefore, the surface of a projected image is more compressed and occupies a smaller area in one view. Since the projective distortion region can not be estimated in terms of a fixed-size matching algorithm, we suggest using a local spatial frequency representation model to address this problem. Instead of matching intensities directly, a Gabor scale-space expansion (scalogram) is used. The scalogram expresses the filter output as a function of the spatial position and the principal wavelength to which the filter is tuned. The phase difference at the corresponding points in the two images is used to find the disparity value. The suggested algorithm provides an analytical closed-form expression for the perspective foreshortening effect. The foreshortening factor is verified to overcome the perspective distortion region. The efficiency and performance of the suggested algorithm for dense depth map reconstruction is demonstrated on the basis of analysis of rectified real images. Hence, our proposed method has a superior performance in comparison with other conventional methods.

6

Amplitude elimination for stereo image matching based on the wavelet approach

Jaworska T.

Machine Graphics and Vision

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2005

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Vol. 14, No. 1

103-120

EN

Point-to-point correspondence is one of the most challenging problems in stereo image matching. Correspondence or disparity established between points of two images is the result of stereo matching. The paper presents new point-to-point correspondence algorithm based on wavelet analysis. Each image in the pair is decomposed into an approximation, and details go through the coarse to fine level. For the above decomposition, multi resolution analysis is used. In the proposed approach, a disparity is found in the wavelet transform space. An extension and generalization of phase-based method is presented. The classical Gabor's approach is extended to real wavelets. Differences of amplitudes (grey level) in images which frequently appear in stereo pair are eliminated. Invariance of the disparity determination with respect to amplitude changes may be achieved by choosing an appropriate pair of wavelet systems. The achieved result is broader than the classical one, based Gabor wavelet and the phase method. Numerical experiments with images have confirmed this approach . Finally, three concepts (see Section 5) are presented to analyse the problem of disparity determination globally.

7

A cooperative stereo matching and occlusion detection algorithm for stereo coding

Han J., Lu Z.

Machine Graphics and Vision

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2004

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Vol. 13, No. 1/2

25-38

EN

This paper presents a novel stereo algorithm for obtaining disparity vectors with simply detected occluded points, which is adaptive to a stereo coding scheme. In this algorithm, we first propose a novel scheme based on an adaptive UT mesh model and an epipolar line constraint principle for stereo matching. Furthermore, a simple occlusion detection algorithm is introduced, which uses two fundamental concepts: the uniqueness assumption and the disparity gradient limit principle. Our technique first extracts some triangular vertices from a reference image using an improved adaptive Delaunay triangulation representation algorithm. As feature points, these vertices are matched in the target image with some correlation measurement. After obtaining the disparity vector of each vertex, the uniqueness assumption and the disparity gradient limit are used to select occluded points and label occluded regions. Thr disparity vectors of the points among the triangular vertices can be calculated by a six-parameter affine transformation. In terms of advantages for image coding of a DT mesh model, this algorithm is definitely appropriate for stereo coding, which has been proven by experimental results. We have applied this algorithm to some stereo images, and the experimental results show that the veracity of the disparity estimation given in this paper is higher than that of the conventional algorithms. What is more. some occluded points and occlusion regions can be easily detected with this algorithm. lu addition, the algorithm can achieve higher coding efficiency as compared to conventional stereo coding algorithms.

8

Novel feature-based stereo matching method that employs tensor representation on local pixels neighborhoods in images

Cyganek B.

Machine Graphics and Vision

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2001

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Vol. 10, No. 3

289-316

EN

Stereo matching techniques have evolved substantially throughout recent years. However, the problem of unambigous stereo points matching, especially in presence of object occlusions, as well as images noise and distortions, remains still open. In this paper, a novel feature-based stereo matching method, based on tensor representation of local structures in digital images, has been described. Application of a structural tensor enables more reliable matching of locally coherent structures, representing averaged dominant gradients in local neighborhoods rather than sparse points. The presented work has been completed with many experiments that confirmed its usefulness, especially in a case of real stereo images.

9

Matching feature points in stereo pairs: a comparative study of some matching strategies

Vincent E., Laganiere R.

Machine Graphics and Vision

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2001

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Vol. 10, No. 3

237-259

EN

Several algorithms are proposed in the literature to solve the difficult problem of feature point correspondence between image pairs. In order to obtain good quality results, they make use of different aproaches and constraints to improve the quality of the matching set. A matching strategy is considered useful if it is able to filter out many of the mismatches found in an input matching set while keeping in most of the good matches present. In this paper, we present a survey of different matching strategies. We propose an empirical evaluation of thier performance. The validation process used here determines the number of good matches and the proportion of good matches in a given match set for the different parameter values of a matching constraint.

10

A new approach to stereo image matching based on multiresolution wavelet analysis

Jaworska T.

Machine Graphics and Vision

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2000

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Vol. 9, No. 1/2

439-446

EN

Automatic stereo matching in an importamt problem and many algorithms have been developed already. The paper presents a new stereo matching algorithm. Correspondence and disparity esablished between points. of two images is the result of stereo matching. The proposed solution is based on wavelet transform. A two-dimensional digital image is a signal which is analyzed in wanelet space. Each image of stereopair is decomposed using multiresolution analysis for many levels from fine-to-coarse. Each image is also decomposed into an approximation and details (vertical, horizontal and diagonal) which are computed using a recursive algorithm of Mallat [8]. In the proposed approach a disparuty is found in the wavelet transform space. The minimization problem which appears in disparity determination is solved using a Hopfield neural network. The neural network is used for finding the disparity separately for approximation and details in the horizontal direction and separately for aproximation and details in the vertical direction. The approach is based on constructing vectors containing coefficients from each level. The number of vectors is equal to the numbers of coefficients at the finest level. Vectors are constructed for coefficients of approximation and for sum of coefficients of approximation and details respectively. A norm of the difference of vectors is set as neurons bias.