A Distributed Mincut/Maxflow Algorithm Combining Path Augmentation and Push-Relabel

We develop a novel distributed algorithm for the minimum cut problem. We primarily aim at solving large sparse problems. Assuming vertices of the graph are partitioned into several regions, the algorithm performs path augmentations inside the regions and updates of the push-relabel style between the regions. The interaction between regions is considered expensive (regions are loaded into the memory one-by-one or located on separate machines in a network). The algorithm works in sweeps - passes over all regions. Let $B$ be the set of vertices incident to inter-region edges of the graph. We present a sequential and parallel versions of the algorithm which terminate in at most $2|B|^2+1$ sweeps. The competing algorithm by Delong and Boykov uses push-relabel updates inside regions. In the case of a fixed partition we prove that this algorithm has a tight $O(n^2)$ bound on the number of sweeps, where $n$ is the number of vertices. We tested sequential versions of the algorithms on instances of maxflow problems in computer vision. Experimentally, the number of sweeps required by the new algorithm is much lower than for the Delong and Boykov's variant. Large problems (up to $10^8$ vertices and $6\cdot 10^8$ edges) are solved using under 1GB of memory in about 10 sweeps.Comment: 40 pages, 15 figure

Adaptive non-linear Predictor for Lossless Image Compression

. The paper proposes the new method for lossless image compression that performs wery well and results can be compared with other methods that we are aware of. We developed further the Slessinger's idea to represent an image as residuals of a special local predictor. The predictor configurations in a binary image are grouped into couples that differ in representative point only. Only residuals that correspond to the less frequent predictor from the couple is stored. An optimal predictor is based on the frequency of predictor configuration in the image. Two main extensions are proposed. (1) The method is generalized for grey-level image or images with even more degrees of freedom. (2) The method that works with addaptive estimator is proposed. The resulting FH-Adapt algorithm performs very well and results could be compared with most of the current algorithms for the same purpose. The predictor can learn automatically from the compressed image and cope even with complicated fine textur..

Training Set Approximation for Kernel Methods

We propose a technique for a training set approximation and its usage in kernel methods. The approach aims to represent data in a low dimensional space with possibly minimal representation error which is similar to the Principal Component Analysis (PCA). In contrast to the PCA, the basis vectors of the low dimensional space used for data representation are properly selected vectors from the training set and not as their linear combinations. The basis vectors can be selected by a simple algorithm which has low computational requirements and allows on-line processing of huge data sets. The proposed method was used to approximate training sets of the Support Vector Machines and Kernel Fisher Linear Discriminant which are known method for learning classifiers. The experiments show that the proposed approximation can significantly reduce the complexity of the found classifiers (the number of the support vectors) while retaining their accuracy

Correspondences from Dense Sequences Allowing to Analyze Epipolar Plane Images

We present the method seeking correspondences in a dense rectified image sequence, considered as a set of Epipolar Plane Images (EPI). The main idea is to employ dense sequence to get more information which could guide the correspondence algorithm. A set of EPIs has properties that are favorable for evaluating the quality of correspondence pair (correspondence cost). Information contained in image data is used directly, no features are detected. Our spatio-temporal volume analysis approach aims at accuracy and density of the correspondences established

Kernel represenation of the Kesler construction for Multi-class SVM classification

We propose a transformation from the multi-class SVM classification problem to the singleclass SVM problem which is more convenient for optimization. The proposed transformation is based on simplifying the original problem and employing the Kesler construction which can be carried out by the use of properly defined kernel only. The experiments conducted indicate that the proposed method is comparable with the one-against-all decomposition solved by the state-of-the-art SMO algorithm

Multi-class Support Vector Machine

classification problem to the single-class SVM problem which is more convenient for optimization. The proposed transformation is based on simplifying the original problem and employing the Kesler construction which can be carried out by the use of properly defined kernel only. The experiments conducted indicate that the proposed method is comparable with the one-against-all decomposition solved by the state-of-the-art SMO algorithm

Image processing, analysis, and machine vision

Bai

Image processing, analysis, and machine vision

xxxv, 870 p. ; 24 cm