This work presents a geometry-based image retrieval approach for multi-object images. We commence with developing an effective shape matching method for closed boundaries. Then, a structured representation, called curvature tree (CT), is introduced to extend the shape matching approach to handle images containing multiple objects with possible holes. We also propose an algorithm, based on Gestalt principles, to detect and extract high-level boundaries (or envelopes), which may evolve as a result of the spatial arrangement of a group of image objects. At first, a shape retrieval method using triangle-area representation (TAR) is presented for non-rigid shapes with closed boundaries. This representation is effective in capturing both local and global characteristics of a shape, invariant to translation, rotation, scaling and shear, and robust against noise and moderate amounts of occlusion. For matching, two algorithms are introduced. The first algorithm matches concavity maxima points extracted from TAR image obtained by thresholding the TAR. In the second matching algorithm, dynamic space warping (DSW) is employed to search efficiently for the optimal (least cost) correspondence between the points of two shapes. Experimental results using the MPEG-7 CE-1 database of 1400 shapes show the superiority of our method over other recent methods. Then, a geometry-based image retrieval system is developed for multi-object images. We model both shape and topology of image objects including holes using a structured representation called curvature tree (CT). To facilitate shape-based matching, the TAR of each object and hole is stored at the corresponding node in the CT. The similarity between two CTs is measured based on the maximum similarity subtree isomorphism (MSSI) where a one-to-one correspondence is established between the nodes of the two trees. Our matching scheme agrees with many recent findings in psychology about the human perception of multi-object images. Two algorithms are introduced to solve the MSSI problem: an approximate and an exact. Both algorithms have polynomial-time computational complexity and use the DSW as the similarity measure between the attributed nodes. Experiments on a database of 13500 medical images and a database of 1580 logo images have shown the effectiveness of the proposed method. The purpose of the last part is to allow for high-level shape retrieval in multi-object images by detecting and extracting the envelope of high-level object groupings in the image. Motivated by studies in Gestalt theory, a new algorithm for the envelope extraction is proposed that works in two stages. The first stage detects the envelope (if exists) and groups its objects using hierarchical clustering. In the second stage, each grouping is merged using morphological operations and then further refined using concavity tree reconstruction to eliminate odd concavities in the extracted envelope. Experiment on a set of 110 logo images demonstrates the feasibility of our approach.

This work presents a geometry-based image retrieval approach for multi-object images. We commence with developing an effective shape matching method for closed boundaries. Then, a structured representation, called curvature tree (CT), is introduced to extend the shape matching approach to handle images containing multiple objects with possible holes. We also propose an algorithm, based on Gestalt principles, to detect and extract high-level boundaries (or envelopes), which may evolve as a result of the spatial arrangement of a group of image objects. At first, a shape retrieval method using triangle-area representation (TAR) is presented for non-rigid shapes with closed boundaries. This representation is effective in capturing both local and global characteristics of a shape, invariant to translation, rotation, scaling and shear, and robust against noise and moderate amounts of occlusion. For matching, two algorithms are introduced. The first algorithm matches concavity maxima points extracted from TAR image obtained by thresholding the TAR. In the second matching algorithm, dynamic space warping (DSW) is employed to search efficiently for the optimal (least cost) correspondence between the points of two shapes. Experimental results using the MPEG-7 CE-1 database of 1400 shapes show the superiority of our method over other recent methods. Then, a geometry-based image retrieval system is developed for multi-object images. We model both shape and topology of image objects including holes using a structured representation called curvature tree (CT). To facilitate shape-based matching, the TAR of each object and hole is stored at the corresponding node in the CT. The similarity between two CTs is measured based on the maximum similarity subtree isomorphism (MSSI) where a one-to-one correspondence is established between the nodes of the two trees. Our matching scheme agrees with many recent findings in psychology about the human perception of multi-object images. Two algorithms are introduced to solve the MSSI problem: an approximate and an exact. Both algorithms have polynomial-time computational complexity and use the DSW as the similarity measure between the attributed nodes. Experiments on a database of 13500 medical images and a database of 1580 logo images have shown the effectiveness of the proposed method. The purpose of the last part is to allow for high-level shape retrieval in multi-object images by detecting and extracting the envelope of high-level object groupings in the image. Motivated by studies in Gestalt theory, a new algorithm for the envelope extraction is proposed that works in two stages. The first stage detects the envelope (if exists) and groups its objects using hierarchical clustering. In the second stage, each grouping is merged using morphological operations and then further refined using concavity tree reconstruction to eliminate odd concavities in the extracted envelope. Experiment on a set of 110 logo images demonstrates the feasibility of our approach.

Η παρούσα εργασία ασχολείται με την ανάκτηση (retrieval) σχήματος από μια βάση δεδομένων στην οποία περιλαμβάνονται ομοειδή αλλά και ανόμοια σχήματα. Τα σχήματα αυτά είναι τρισδιάστατα και παρουσιάζονται σε διάφορες μορφές. Αυτό σημαίνει ότι το ίδιο αντικείμενο μπορεί να παρουσιάζεται στην βάση δεδομένων είτε ελαφρώς παραμορφωμένο, είτε από διαφορετική γωνία είτε να έχουν μετατοπιστεί οι κινούμενοι σύνδεσμοι που μπορεί να έχει. Πρόκληση και στόχος αυτής της διπλωματικής εργασίας είναι ο αλγόριθμος που θα υλοποιήσουμε, να μπορεί να ταυτοποιεί το προς εξέταση αντικείμενο με τα σχήματα που αντιπροσωπεύουν το αυτό αντικείμενο. Ο αλγόριθμος που θα χρησιμοποιήσουμε κάνει χρήση των αποστάσεων διάχυσης (Diffusion distances), οι οποίες αποτελούν αντικείμενο έρευνας με πολλές εφαρμογές για την ανεύρεση σχήματος. / This paper deals with the retrieval of shapes from a database that includes similar and dissimilar shapes. These shapes are three-dimensional and are presented in various forms. This means that the same object can be presented in the database or slightly distorted, either from a different angle or with the driven links shifted. Challenge and aim of this thesis is the algorithm that we will implement , it can identify the subject being studied with shapes that represent the same object. The algorithm makes use of the diffusion distances, which are the subject of investigation of many applications for finding shape.

Shape is very essential for detecting and recognizing objects. It is robust to illumination, color changes. Human can recognize objects just based on shapes, thus shape based object detection and recognition methods have been popular in many years. Due to problem of segmentation, some researchers have worked on silhouettes instead of real images. The main problem in this area is object recognition and the difficulty is to handle shapes articulation and distortion. Previous methods mainly focus on one to one shape similarity measurement, which ignores context information between shapes. Instead, we utilize graph-transduction methods to reveal the intrinsic relation between shapes on 'shape manifold'. Our methods consider the context information in the dataset, which improves the performance a lot. To better describe the manifold structure, we also propose a novel method to add synthetic data points for densifying data manifold. The experimental results have shown the advantage of the algorithm. Moreover, a novel diffusion process on Tensor Product Graph is carried out for learning better affinities between data. This is also used for shape retrieval, which reaches the best ever results on MPEG-7 dataset. As shapes are important and helpful for object detection and recognition in real images, a lot of methods have used shapes to detect and recognize objects. There are two important parts for shape based methods, model construction and object detection, recognition. Most of the current methods are based on hand selected models, which is helpful but not extendable. To solve this problem, we propose to construct model by shape matching between some silhouettes and one hand decomposed silhouette. This weakly supervised method can be used not only learn the models in one object class, but also transfer the structure knowledge to other classes, which has the similar structure with the hand decomposed silhouette. The other problem is detecting and recognizing objects. A lot of methods search the images by sliding window to detect objects, which can find the global solution but with high complexity. Instead, we use sampling methods to reduce the complexity. The method we utilized is particle filter, which is popular in robot mapping and localization. We modified the standard particle filter to make it suitable for static observations and it is very helpful for object detection. Moreover, The usage of particle filter is extended for solving the jigsaw puzzle problem, where puzzle pieces are square image patches. The proposed method is able to reach much better results than the method with Loopy Belief Propagation. / Computer and Information Science

Com o aumento da capacidade de armazenamento de informação em bancos de dados e em computadores pessoais, surge a necessidade de algoritmos computacionais capazes de realizar o processamento automático para recuperação desses dados. Esse fato não é diferente para objetos tridimensionais armazenados em formato de arquivos. Nesta Dissertação de Mestrado foram estudadas novas técnicas para processamento desses objetos utilizando uma abordagem não comum à área: técnicas para análise de séries temporais, tais como scattering wavelets e gráficos de recorrência. No caso de recuperação total de objetos, ou seja, dado uma malha tridimensional encontrar outras malhas que são visualmente semelhantes, uma única característica é extraída curvatura gaussiana e variação de superfície, por exemplo e ordenada como uma série com a informação provida pelo vetor de Fiedler. Então processa-se essa série utilizando a técnica scattering wavelets, que são capazes de analisar o comportamento temporal de conjunto de dados seriais. Para esse problema, os resultados obtidos são comparáveis com outras abordagens apresentadas na literatura que utilizam várias características para se chegar ao resultado. Já no caso de recuperação parcial de objetos, em que apenas uma parte do objeto é dado como parâmetro de busca, é necessário realizar uma segmentação das malhas para se encontrar outras partes que são visualmente semelhantes. Ao utilizarmos um gráfico de recorrência para analisar os objetos, é possível encontrar não apenas a região mais semelhante dentro da mesma (ou de outra) malha, mas também se obtém todas as regiões que são similares ao parâmetro de busca. / With the increasing data storage capacity of databases and personal computers, arises the necessity of computer algorithms capable of performing processing for automatic recovery of data and information. This fact is no different for three-dimensional objects stored in files. In this Masters Thesis we studied new techniques for processing such data objects using an unusual approach to the geometric processing area: techniques for analyzing time series, such as scattering wavelets and recurrence plots. For shape retrieval problem, i.e., given a tridimensional mesh try finding other meshes that are visually similar, our method extract only one feature Gaussian curvature and surface variation, for example and organize it as a series using information given by Fiedler vector. Then, the next step is to process the resulting series using a technique called scattering wavelets, that is capable of analyzing the temporal behavior of a set of serial data. For this problem, the results are comparable with other approaches reported in the literature that use multiple characteristics to find a matching mesh. In the case of partial retrieval of objects, in which only a part of the object is given as search parameter, it is necessary to perform a segmentation of the meshes in order to find other parts that are visually similar to the query. By using Recurrence Plot to analyze the objects, our method can find not only the most similar region within the same (or other) object, but also get all the regions that are similar to the search parameter.

Com o aumento da capacidade de armazenamento de informação em bancos de dados e em computadores pessoais, surge a necessidade de algoritmos computacionais capazes de realizar o processamento automático para recuperação desses dados. Esse fato não é diferente para objetos tridimensionais armazenados em formato de arquivos. Nesta Dissertação de Mestrado foram estudadas novas técnicas para processamento desses objetos utilizando uma abordagem não comum à área: técnicas para análise de séries temporais, tais como scattering wavelets e gráficos de recorrência. No caso de recuperação total de objetos, ou seja, dado uma malha tridimensional encontrar outras malhas que são visualmente semelhantes, uma única característica é extraída curvatura gaussiana e variação de superfície, por exemplo e ordenada como uma série com a informação provida pelo vetor de Fiedler. Então processa-se essa série utilizando a técnica scattering wavelets, que são capazes de analisar o comportamento temporal de conjunto de dados seriais. Para esse problema, os resultados obtidos são comparáveis com outras abordagens apresentadas na literatura que utilizam várias características para se chegar ao resultado. Já no caso de recuperação parcial de objetos, em que apenas uma parte do objeto é dado como parâmetro de busca, é necessário realizar uma segmentação das malhas para se encontrar outras partes que são visualmente semelhantes. Ao utilizarmos um gráfico de recorrência para analisar os objetos, é possível encontrar não apenas a região mais semelhante dentro da mesma (ou de outra) malha, mas também se obtém todas as regiões que são similares ao parâmetro de busca. / With the increasing data storage capacity of databases and personal computers, arises the necessity of computer algorithms capable of performing processing for automatic recovery of data and information. This fact is no different for three-dimensional objects stored in files. In this Masters Thesis we studied new techniques for processing such data objects using an unusual approach to the geometric processing area: techniques for analyzing time series, such as scattering wavelets and recurrence plots. For shape retrieval problem, i.e., given a tridimensional mesh try finding other meshes that are visually similar, our method extract only one feature Gaussian curvature and surface variation, for example and organize it as a series using information given by Fiedler vector. Then, the next step is to process the resulting series using a technique called scattering wavelets, that is capable of analyzing the temporal behavior of a set of serial data. For this problem, the results are comparable with other approaches reported in the literature that use multiple characteristics to find a matching mesh. In the case of partial retrieval of objects, in which only a part of the object is given as search parameter, it is necessary to perform a segmentation of the meshes in order to find other parts that are visually similar to the query. By using Recurrence Plot to analyze the objects, our method can find not only the most similar region within the same (or other) object, but also get all the regions that are similar to the search parameter.

Modelos geométricos desempenham um papel fundamental em divérsas áreas, desde a indústria do entretenimento até aplicações científicas. Para reduzir o elevado custo de criação de um modelo 3D, a reutilização de modelos existentes é a solução ideal. Recuperação de modelos 3D utilizam técnicas baseadas em conteúdo (do inglês CBR) que auxiliam a busca de modelos desejados em repositórios massivos, muitos disponíveis publicamente na Internet. Pontos principais para técnicas CBR eficientes e eficazes são descritores de forma que capturam com precisão as características de uma forma 3D e são capazes de discriminar entre diferentes formas. Nós apresentamos um descritor com base na distribuição de duas características globais, extraídas de uma forma 3D, depth complexity e thickness, que, respectivamente, capturam aspectos da topologia e da geometria das formas 3D. O descritor final, chamado DCT (depth complexity and thickness histogram), é um histograma 2D invariante a translações, rotações e escalas das formas geométricas. Nós eficientemente implementamos o DCT na GPU, permitindo sua utilização em consultas em tempo real em grandes bases de dados de modelos 3D. Nós validamos o DCT com as Princeton e Toyohashi Forma Benchmarks, contendo 1815 e 10000 modelos respectivamente. Os resultados mostram que DCT pode discriminar classes significativas desses benchmarks, é rápido e robusto contra transformações de forma e diferentes níveis de subdivisão e suavidade dos modelos. / Geometric models play a vital role in several fields, from the entertainment industry to scientific applications. To reduce the high cost of model creation, reusing existing models is the solution of choice. Model reuse is supported by content-based shape retrieval (CBR) techniques that help finding the desired models in massive repositories, many publicly available on the Internet. Key to efficient and effective CBR techniques are shape descriptors that accurately capture the characteristics of a shape and are able to discriminate between different shapes. We present a descriptor based on the distribution of two global features measured on a 3D shape, depth complexity and thickness, which respectively capture aspects of the geometry and topology of 3D shapes. The final descriptor, called DCT (depth complexity and thickness histogram), is a 2D histogram that is invariant to the translation, rotation and scale of geometric shapes. We efficiently implement the DCT on the GPU, allowing its use in real-time queries of large model databases. We validate the DCT with the Princeton and Toyohashi Shape Benchmarks, containing 1815 and 10000 models respectively. Results show that DCT can discriminate meaningful classes of these benchmarks, and is fast to compute and robust against shape transformations and different levels of subdivision and smoothness.

Modelos geométricos desempenham um papel fundamental em divérsas áreas, desde a indústria do entretenimento até aplicações científicas. Para reduzir o elevado custo de criação de um modelo 3D, a reutilização de modelos existentes é a solução ideal. Recuperação de modelos 3D utilizam técnicas baseadas em conteúdo (do inglês CBR) que auxiliam a busca de modelos desejados em repositórios massivos, muitos disponíveis publicamente na Internet. Pontos principais para técnicas CBR eficientes e eficazes são descritores de forma que capturam com precisão as características de uma forma 3D e são capazes de discriminar entre diferentes formas. Nós apresentamos um descritor com base na distribuição de duas características globais, extraídas de uma forma 3D, depth complexity e thickness, que, respectivamente, capturam aspectos da topologia e da geometria das formas 3D. O descritor final, chamado DCT (depth complexity and thickness histogram), é um histograma 2D invariante a translações, rotações e escalas das formas geométricas. Nós eficientemente implementamos o DCT na GPU, permitindo sua utilização em consultas em tempo real em grandes bases de dados de modelos 3D. Nós validamos o DCT com as Princeton e Toyohashi Forma Benchmarks, contendo 1815 e 10000 modelos respectivamente. Os resultados mostram que DCT pode discriminar classes significativas desses benchmarks, é rápido e robusto contra transformações de forma e diferentes níveis de subdivisão e suavidade dos modelos. / Geometric models play a vital role in several fields, from the entertainment industry to scientific applications. To reduce the high cost of model creation, reusing existing models is the solution of choice. Model reuse is supported by content-based shape retrieval (CBR) techniques that help finding the desired models in massive repositories, many publicly available on the Internet. Key to efficient and effective CBR techniques are shape descriptors that accurately capture the characteristics of a shape and are able to discriminate between different shapes. We present a descriptor based on the distribution of two global features measured on a 3D shape, depth complexity and thickness, which respectively capture aspects of the geometry and topology of 3D shapes. The final descriptor, called DCT (depth complexity and thickness histogram), is a 2D histogram that is invariant to the translation, rotation and scale of geometric shapes. We efficiently implement the DCT on the GPU, allowing its use in real-time queries of large model databases. We validate the DCT with the Princeton and Toyohashi Shape Benchmarks, containing 1815 and 10000 models respectively. Results show that DCT can discriminate meaningful classes of these benchmarks, and is fast to compute and robust against shape transformations and different levels of subdivision and smoothness.

Modelos geométricos desempenham um papel fundamental em divérsas áreas, desde a indústria do entretenimento até aplicações científicas. Para reduzir o elevado custo de criação de um modelo 3D, a reutilização de modelos existentes é a solução ideal. Recuperação de modelos 3D utilizam técnicas baseadas em conteúdo (do inglês CBR) que auxiliam a busca de modelos desejados em repositórios massivos, muitos disponíveis publicamente na Internet. Pontos principais para técnicas CBR eficientes e eficazes são descritores de forma que capturam com precisão as características de uma forma 3D e são capazes de discriminar entre diferentes formas. Nós apresentamos um descritor com base na distribuição de duas características globais, extraídas de uma forma 3D, depth complexity e thickness, que, respectivamente, capturam aspectos da topologia e da geometria das formas 3D. O descritor final, chamado DCT (depth complexity and thickness histogram), é um histograma 2D invariante a translações, rotações e escalas das formas geométricas. Nós eficientemente implementamos o DCT na GPU, permitindo sua utilização em consultas em tempo real em grandes bases de dados de modelos 3D. Nós validamos o DCT com as Princeton e Toyohashi Forma Benchmarks, contendo 1815 e 10000 modelos respectivamente. Os resultados mostram que DCT pode discriminar classes significativas desses benchmarks, é rápido e robusto contra transformações de forma e diferentes níveis de subdivisão e suavidade dos modelos. / Geometric models play a vital role in several fields, from the entertainment industry to scientific applications. To reduce the high cost of model creation, reusing existing models is the solution of choice. Model reuse is supported by content-based shape retrieval (CBR) techniques that help finding the desired models in massive repositories, many publicly available on the Internet. Key to efficient and effective CBR techniques are shape descriptors that accurately capture the characteristics of a shape and are able to discriminate between different shapes. We present a descriptor based on the distribution of two global features measured on a 3D shape, depth complexity and thickness, which respectively capture aspects of the geometry and topology of 3D shapes. The final descriptor, called DCT (depth complexity and thickness histogram), is a 2D histogram that is invariant to the translation, rotation and scale of geometric shapes. We efficiently implement the DCT on the GPU, allowing its use in real-time queries of large model databases. We validate the DCT with the Princeton and Toyohashi Shape Benchmarks, containing 1815 and 10000 models respectively. Results show that DCT can discriminate meaningful classes of these benchmarks, and is fast to compute and robust against shape transformations and different levels of subdivision and smoothness.

Cette thèse porte sur l’appariement des formes, et la recherche par forme clef. Elle décrit quatrecontributions à ce domaine. La première contribution est une amélioration de la méthode des nuéesdynamiques pour partitionner au mieux les voxels à l’intérieur d’une forme donnée ; les partitionsobtenues permettent d’apparier les objets par un couplage optimal dans un graphe biparti. Laseconde contribution est la fusion de deux descripteurs, l’un local, l’autre global, par la règle duproduit. La troisième contribution considère le graphe complet, dont les sommets sont les formes dela base ou la requête, et les arêtes sont étiquetées par plusieurs distances, une par descripteur ;ensuite cette méthode calcule par programmation linéaire la combinaison convexe des distancesqui maximise soit la somme des longueurs des plus courts chemins entre la requête et les objetsde la base de données, soit la longueur du plus court chemin entre la requête et l’objet comparé àla requête. La quatrième contribution consiste à perturber la requête avec un algorithme génétiquepour la rapprocher des formes de la base de données, pour un ou des descripteur(s) donné(s) ; cetteméthode est massivement parallèle, et une architecture multi-agent est proposée. Ces méthodes sontcomparées aux méthodes classiques, et ont de meilleures performances, en terme de précision. / This thesis concerns shape matching and shape retrieval. It describes four contributions to thisdomain. The first is an improvement of the k-means method, in order to find the best partition ofvoxels inside a given shape ; these best partitions permit to match shapes using an optimal matchingin a bipartite graph. The second contribution is the fusion of two descriptors, one local, the otherglobal, with the product rule. The third contribution considers the complete graph, the vertices ofwhich are the shapes in the database and the query. Edges are labelled with several distances,one per descriptor. Then the method computes, with linear programming, the convex combinationof distances which maximizes either the sum of the lengths of all shortest paths from the query toall shapes of the database, or the length of the shortest path in the graph from query to the currentshape compared to query. The fourth contribution consists in perturbing the shape query, to make itcloser to shapes in the database, for any given descriptors. This method is massively parallel and amulti-agent architecture is proposed. These methods are compared to classical methods in the field,they achieve better retrieval performances.