Product graph-based higher order contextual similarities for inexact subgraph matching

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record Many algorithms formulate graph matching as an optimization of an objective function of pairwise quantification of nodes and edges of two graphs to be matched. Pairwise measurements usually consider local attributes but disregard contextual information involved in graph structures. We address this issue by proposing contextual similarities between pairs of nodes. This is done by considering the tensor product graph (TPG) of two graphs to be matched, where each node is an ordered pair of nodes of the operand graphs. Contextual similarities between a pair of nodes are computed by accumulating weighted walks (normalized pairwise similarities) terminating at the corresponding paired node in TPG. Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG. We use contextual similarities to construct an objective function and optimize it with a linear programming approach. Since random walk formulation through TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities and better discrimination among the nodes and edges. Experimental results shown on synthetic as well as real benchmarks illustrate that higher order contextual similarities increase discriminating power and allow one to find approximate solutions to the subgraph matching problem.European Union Horizon 202

Інтерактивна система розпізнавання 3D об’єктів

Пояснювальна записка дипломного проекту складається з чотирьох розділів, містить 108 сторінок, 22 рисунки, 6 таблиць, 159 джерел, 9 ілюстративних матеріалів – загалом 108 сторінок. Об`єкт дослідження: 3D-об’єкти. Мета магістерської дисертації: підвищення ефективності системи розпізнавання тривимірних об’єктів, на основі аналізу двовимірних зображень. У вступі викладена мета, об’єкт і предмет дослідження, актуальність та новизна дисертації. Перший розділ містить аналіз сучасного стану систем розпізнавання просторових об’єктів. У другому розділі розглянуто та проаналізовано модифікований метод розпізнавання просторових об’єктів. У третьому розділі описано розробку структури та елементів інтерактивної системи розпізнавання тривимірних об’єктів. Четвертий розділ містить дослідження інтерактивної системи розпізнавання 3d-об’єктів.The explanatory note of the diploma project consists of four sections, contains 108 pages, 22 figures, 6 tables, 159 sources, 9 illustrative materials - a total of 108 pages. Object of research: 3D objects. The purpose of the master's dissertation: to increase the efficiency of the system of recognition of three-dimensional objects, based on the analysis of two-dimensional images. The introduction outlines the purpose, object and subject of research, relevance and novelty of the dissertation. The first section provides an analysis of the current state of spatial object recognition systems. The second section discusses and analyzes a modified method of spatial object recognition. The third section describes the development of the structure and elements of an interactive system for recognizing three-dimensional objects. The fourth section contains research on an interactive 3D object recognition system

Optimal Object Matching via Convexification and Composition

In this paper, we propose a novel object matching method to match an object to its instance in an input scene image, where both the object template and the input scene image are represented by groups of feature points. We relax each template point’s discrete feature cost function to create a convex function that can be optimized efficiently. Such continuous and convex functions with different regularization terms are able to create different convex optimization models handling objects undergoing (i) global transformation, (ii) locally affine transformation, and (iii) articulated transformation. These models can better constrain each template point’s transformation and therefore generate more robust matching results. Unlike traditional object or feature matching methods with “hard ” node-to-node results, our proposed method allows template points to be transformed to any location in the image plane. Such a property makes our method robust to feature point occlusion or mis-detection. Our extensive experiments demonstrate the robustness and flexibility of our method. 1