Shape Analysis Using Spectral Geometry

Shape analysis is a fundamental research topic in computer graphics and computer vision. To date, more and more 3D data is produced by those advanced acquisition capture devices, e.g., laser scanners, depth cameras, and CT/MRI scanners. The increasing data demands advanced analysis tools including shape matching, retrieval, deformation, etc. Nevertheless, 3D Shapes are represented with Euclidean transformations such as translation, scaling, and rotation and digital mesh representations are irregularly sampled. The shape can also deform non-linearly and the sampling may vary. In order to address these challenging problems, we investigate Laplace-Beltrami shape spectra from the differential geometry perspective, focusing more on the intrinsic properties. In this dissertation, the shapes are represented with 2 manifolds, which are differentiable. First, we discuss in detail about the salient geometric feature points in the Laplace-Beltrami spectral domain instead of traditional spatial domains. Simultaneously, the local shape descriptor of a feature point is the Laplace-Beltrami spectrum of the spatial region associated to the point, which are stable and distinctive. The salient spectral geometric features are invariant to spatial Euclidean transforms, isometric deformations and mesh triangulations. Both global and partial matching can be achieved with these salient feature points. Next, we introduce a novel method to analyze a set of poses, i.e., near-isometric deformations, of 3D models that are unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectral one where all near isometric deformations, mesh triangulations and Euclidean transformations are filtered away. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectral domain while semantic skeleton can be automatically built with joints detected. Finally we prove the shape spectrum is a continuous function to a scale function on the conformal factor of the manifold. The derivatives of the eigenvalues are analytically expressed with those of the scale function. The property applies to both continuous domain and discrete triangle meshes. On the triangle meshes, a spectrum alignment algorithm is developed. Given two closed triangle meshes, the eigenvalues can be aligned from one to the other and the eigenfunction distributions are aligned as well. This extends the shape spectra across non-isometric deformations, supporting a registration-free analysis of general motion data

Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure

Biologically motivated keypoint detection for RGB-D data

With the emerging interest in active vision, computer vision researchers have been increasingly concerned with the mechanisms of attention. Therefore, several visual attention computational models inspired by the human visual system, have been developed, aiming at the detection of regions of interest in images. This thesis is focused on selective visual attention, which provides a mechanism for the brain to focus computational resources on an object at a time, guided by low-level image properties (Bottom-Up attention). The task of recognizing objects in different locations is achieved by focusing on different locations, one at a time. Given the computational requirements of the models proposed, the research in this area has been mainly of theoretical interest. More recently, psychologists, neurobiologists and engineers have developed cooperation's and this has resulted in considerable benefits. The first objective of this doctoral work is to bring together concepts and ideas from these different research areas, providing a study of the biological research on human visual system and a discussion of the interdisciplinary knowledge in this area, as well as the state-of-art on computational models of visual attention (bottom-up). Normally, the visual attention is referred by engineers as saliency: when people fix their look in a particular region of the image, that's because that region is salient. In this research work, saliency methods are presented based on their classification (biological plausible, computational or hybrid) and in a chronological order. A few salient structures can be used for applications like object registration, retrieval or data simplification, being possible to consider these few salient structures as keypoints when aiming at performing object recognition. Generally, object recognition algorithms use a large number of descriptors extracted in a dense set of points, which comes along with very high computational cost, preventing real-time processing. To avoid the problem of the computational complexity required, the features have to be extracted from a small set of points, usually called keypoints. The use of keypoint-based detectors allows the reduction of the processing time and the redundancy in the data. Local descriptors extracted from images have been extensively reported in the computer vision literature. Since there is a large set of keypoint detectors, this suggests the need of a comparative evaluation between them. In this way, we propose to do a description of 2D and 3D keypoint detectors, 3D descriptors and an evaluation of existing 3D keypoint detectors in a public available point cloud library with 3D real objects. The invariance of the 3D keypoint detectors was evaluated according to rotations, scale changes and translations. This evaluation reports the robustness of a particular detector for changes of point-of-view and the criteria used are the absolute and the relative repeatability rate. In our experiments, the method that achieved better repeatability rate was the ISS3D method. The analysis of the human visual system and saliency maps detectors with biological inspiration led to the idea of making an extension for a keypoint detector based on the color information in the retina. Such proposal produced a 2D keypoint detector inspired by the behavior of the early visual system. Our method is a color extension of the BIMP keypoint detector, where we include both color and intensity channels of an image: color information is included in a biological plausible way and multi-scale image features are combined into a single keypoints map. This detector is compared against state-of-art detectors and found particularly well-suited for tasks such as category and object recognition. The recognition process is performed by comparing the extracted 3D descriptors in the locations indicated by the keypoints after mapping the 2D keypoints locations to the 3D space. The evaluation allowed us to obtain the best pair keypoint detector/descriptor on a RGB-D object dataset. Using our keypoint detector and the SHOTCOLOR descriptor a good category recognition rate and object recognition rate were obtained, and it is with the PFHRGB descriptor that we obtain the best results. A 3D recognition system involves the choice of keypoint detector and descriptor. A new method for the detection of 3D keypoints on point clouds is presented and a benchmarking is performed between each pair of 3D keypoint detector and 3D descriptor to evaluate their performance on object and category recognition. These evaluations are done in a public database of real 3D objects. Our keypoint detector is inspired by the behavior and neural architecture of the primate visual system: the 3D keypoints are extracted based on a bottom-up 3D saliency map, which is a map that encodes the saliency of objects in the visual environment. The saliency map is determined by computing conspicuity maps (a combination across different modalities) of the orientation, intensity and color information, in a bottom-up and in a purely stimulusdriven manner. These three conspicuity maps are fused into a 3D saliency map and, finally, the focus of attention (or "keypoint location") is sequentially directed to the most salient points in this map. Inhibiting this location automatically allows the system to attend to the next most salient location. The main conclusions are: with a similar average number of keypoints, our 3D keypoint detector outperforms the other eight 3D keypoint detectors evaluated by achiving the best result in 32 of the evaluated metrics in the category and object recognition experiments, when the second best detector only obtained the best result in 8 of these metrics. The unique drawback is the computational time, since BIK-BUS is slower than the other detectors. Given that differences are big in terms of recognition performance, size and time requirements, the selection of the keypoint detector and descriptor has to be matched to the desired task and we give some directions to facilitate this choice. After proposing the 3D keypoint detector, the research focused on a robust detection and tracking method for 3D objects by using keypoint information in a particle filter. This method consists of three distinct steps: Segmentation, Tracking Initialization and Tracking. The segmentation is made to remove all the background information, reducing the number of points for further processing. In the initialization, we use a keypoint detector with biological inspiration. The information of the object that we want to follow is given by the extracted keypoints. The particle filter does the tracking of the keypoints, so with that we can predict where the keypoints will be in the next frame. In a recognition system, one of the problems is the computational cost of keypoint detectors with this we intend to solve this problem. The experiments with PFBIKTracking method are done indoors in an office/home environment, where personal robots are expected to operate. The Tracking Error evaluates the stability of the general tracking method. We also quantitatively evaluate this method using a "Tracking Error". Our evaluation is done by the computation of the keypoint and particle centroid. Comparing our system that the tracking method which exists in the Point Cloud Library, we archive better results, with a much smaller number of points and computational time. Our method is faster and more robust to occlusion when compared to the OpenniTracker.Com o interesse emergente na visão ativa, os investigadores de visão computacional têm estado cada vez mais preocupados com os mecanismos de atenção. Por isso, uma série de modelos computacionais de atenção visual, inspirado no sistema visual humano, têm sido desenvolvidos. Esses modelos têm como objetivo detetar regiões de interesse nas imagens. Esta tese está focada na atenção visual seletiva, que fornece um mecanismo para que o cérebro concentre os recursos computacionais num objeto de cada vez, guiado pelas propriedades de baixo nível da imagem (atenção Bottom-Up). A tarefa de reconhecimento de objetos em diferentes locais é conseguida através da concentração em diferentes locais, um de cada vez. Dados os requisitos computacionais dos modelos propostos, a investigação nesta área tem sido principalmente de interesse teórico. Mais recentemente, psicólogos, neurobiólogos e engenheiros desenvolveram cooperações e isso resultou em benefícios consideráveis. No início deste trabalho, o objetivo é reunir os conceitos e ideias a partir dessas diferentes áreas de investigação. Desta forma, é fornecido o estudo sobre a investigação da biologia do sistema visual humano e uma discussão sobre o conhecimento interdisciplinar da matéria, bem como um estado de arte dos modelos computacionais de atenção visual (bottom-up). Normalmente, a atenção visual é denominada pelos engenheiros como saliência, se as pessoas fixam o olhar numa determinada região da imagem é porque esta região é saliente. Neste trabalho de investigação, os métodos saliência são apresentados em função da sua classificação (biologicamente plausível, computacional ou híbrido) e numa ordem cronológica. Algumas estruturas salientes podem ser usadas, em vez do objeto todo, em aplicações tais como registo de objetos, recuperação ou simplificação de dados. É possível considerar estas poucas estruturas salientes como pontos-chave, com o objetivo de executar o reconhecimento de objetos. De um modo geral, os algoritmos de reconhecimento de objetos utilizam um grande número de descritores extraídos num denso conjunto de pontos. Com isso, estes têm um custo computacional muito elevado, impedindo que o processamento seja realizado em tempo real. A fim de evitar o problema da complexidade computacional requerido, as características devem ser extraídas a partir de um pequeno conjunto de pontos, geralmente chamados pontoschave. O uso de detetores de pontos-chave permite a redução do tempo de processamento e a quantidade de redundância dos dados. Os descritores locais extraídos a partir das imagens têm sido amplamente reportados na literatura de visão por computador. Uma vez que existe um grande conjunto de detetores de pontos-chave, sugere a necessidade de uma avaliação comparativa entre eles. Desta forma, propomos a fazer uma descrição dos detetores de pontos-chave 2D e 3D, dos descritores 3D e uma avaliação dos detetores de pontos-chave 3D existentes numa biblioteca de pública disponível e com objetos 3D reais. A invariância dos detetores de pontoschave 3D foi avaliada de acordo com variações nas rotações, mudanças de escala e translações. Essa avaliação retrata a robustez de um determinado detetor no que diz respeito às mudanças de ponto-de-vista e os critérios utilizados são as taxas de repetibilidade absoluta e relativa. Nas experiências realizadas, o método que apresentou melhor taxa de repetibilidade foi o método ISS3D. Com a análise do sistema visual humano e dos detetores de mapas de saliência com inspiração biológica, surgiu a ideia de se fazer uma extensão para um detetor de ponto-chave com base na informação de cor na retina. A proposta produziu um detetor de ponto-chave 2D inspirado pelo comportamento do sistema visual. O nosso método é uma extensão com base na cor do detetor de ponto-chave BIMP, onde se incluem os canais de cor e de intensidade de uma imagem. A informação de cor é incluída de forma biológica plausível e as características multi-escala da imagem são combinadas num único mapas de pontos-chave. Este detetor é comparado com os detetores de estado-da-arte e é particularmente adequado para tarefas como o reconhecimento de categorias e de objetos. O processo de reconhecimento é realizado comparando os descritores 3D extraídos nos locais indicados pelos pontos-chave. Para isso, as localizações do pontos-chave 2D têm de ser convertido para o espaço 3D. Isto foi possível porque o conjunto de dados usado contém a localização de cada ponto de no espaço 2D e 3D. A avaliação permitiu-nos obter o melhor par detetor de ponto-chave/descritor num RGB-D object dataset. Usando o nosso detetor de ponto-chave e o descritor SHOTCOLOR, obtemos uma noa taxa de reconhecimento de categorias e para o reconhecimento de objetos é com o descritor PFHRGB que obtemos os melhores resultados. Um sistema de reconhecimento 3D envolve a escolha de detetor de ponto-chave e descritor, por isso é apresentado um novo método para a deteção de pontos-chave em nuvens de pontos 3D e uma análise comparativa é realizada entre cada par de detetor de ponto-chave 3D e descritor 3D para avaliar o desempenho no reconhecimento de categorias e de objetos. Estas avaliações são feitas numa base de dados pública de objetos 3D reais. O nosso detetor de ponto-chave é inspirado no comportamento e na arquitetura neural do sistema visual dos primatas. Os pontos-chave 3D são extraídas com base num mapa de saliências 3D bottom-up, ou seja, um mapa que codifica a saliência dos objetos no ambiente visual. O mapa de saliência é determinada pelo cálculo dos mapas de conspicuidade (uma combinação entre diferentes modalidades) da orientação, intensidade e informações de cor de forma bottom-up e puramente orientada para o estímulo. Estes três mapas de conspicuidade são fundidos num mapa de saliência 3D e, finalmente, o foco de atenção (ou "localização do ponto-chave") está sequencialmente direcionado para os pontos mais salientes deste mapa. Inibir este local permite que o sistema automaticamente orientado para próximo local mais saliente. As principais conclusões são: com um número médio similar de pontos-chave, o nosso detetor de ponto-chave 3D supera os outros oito detetores de pontos-chave 3D avaliados, obtendo o melhor resultado em 32 das métricas avaliadas nas experiências do reconhecimento das categorias e dos objetos, quando o segundo melhor detetor obteve apenas o melhor resultado em 8 dessas métricas. A única desvantagem é o tempo computacional, uma vez que BIK-BUS é mais lento do que os outros detetores. Dado que existem grandes diferenças em termos de desempenho no reconhecimento, de tamanho e de tempo, a seleção do detetor de ponto-chave e descritor tem de ser interligada com a tarefa desejada e nós damos algumas orientações para facilitar esta escolha neste trabalho de investigação. Depois de propor um detetor de ponto-chave 3D, a investigação incidiu sobre um método robusto de deteção e tracking de objetos 3D usando as informações dos pontos-chave num filtro de partículas. Este método consiste em três etapas distintas: Segmentação, Inicialização do Tracking e Tracking. A segmentação é feita de modo a remover toda a informação de fundo, a fim de reduzir o número de pontos para processamento futuro. Na inicialização, usamos um detetor de ponto-chave com inspiração biológica. A informação do objeto que queremos seguir é dada pelos pontos-chave extraídos. O filtro de partículas faz o acompanhamento dos pontoschave, de modo a se poder prever onde os pontos-chave estarão no próximo frame. As experiências com método PFBIK-Tracking são feitas no interior, num ambiente de escritório/casa, onde se espera que robôs pessoais possam operar. Também avaliado quantitativamente este método utilizando um "Tracking Error". A avaliação passa pelo cálculo das centróides dos pontos-chave e das partículas. Comparando o nosso sistema com o método de tracking que existe na biblioteca usada no desenvolvimento, nós obtemos melhores resultados, com um número muito menor de pontos e custo computacional. O nosso método é mais rápido e mais robusto em termos de oclusão, quando comparado com o OpenniTracker

Object Recognition

Vision-based object recognition tasks are very familiar in our everyday activities, such as driving our car in the correct lane. We do these tasks effortlessly in real-time. In the last decades, with the advancement of computer technology, researchers and application developers are trying to mimic the human's capability of visually recognising. Such capability will allow machine to free human from boring or dangerous jobs

Machine learning methods for 3D object classification and segmentation

Field of study: Computer science.Dr. Ye Duan, Thesis Supervisor.Includes vita."July 2018."Object understanding is a fundamental problem in computer vision and it has been extensively researched in recent years thanks to the availability of powerful GPUs and labelled data, especially in the context of images. However, 3D object understanding is still not on par with its 2D domain and deep learning for 3D has not been fully explored yet. In this dissertation, I work on two approaches, both of which advances the state-of-the-art results in 3D classification and segmentation. The first approach, called MVRNN, is based multi-view paradigm. In contrast to MVCNN which does not generate consistent result across different views, by treating the multi-view images as a temporal sequence, our MVRNN correlates the features and generates coherent segmentation across different views. MVRNN demonstrated state-of-the-art performance on the Princeton Segmentation Benchmark dataset. The second approach, called PointGrid, is a hybrid method which combines points and regular grid structure. 3D points can retain fine details but irregular, which is challenge for deep learning methods. Volumetric grid is simple and has regular structure, but does not scale well with data resolution. Our PointGrid, which is simple, allows the fine details to be consumed by normal convolutions under a coarser resolution grid. PointGrid achieved state-of-the-art performance on ModelNet40 and ShapeNet datasets in 3D classification and object part segmentation.Includes bibliographical references (pages 116-140)

3D object retrieval and segmentation: various approaches including 2D poisson histograms and 3D electrical charge distributions.

Nowadays 3D models play an important role in many applications: viz. games, cultural heritage, medical imaging etc. Due to the fast growth in the number of available 3D models, understanding, searching and retrieving such models have become interesting fields within computer vision. In order to search and retrieve 3D models, we present two different approaches: one is based on solving the Poisson Equation over 2D silhouettes of the models. This method uses 60 different silhouettes, which are automatically extracted from different viewangles. Solving the Poisson equation for each silhouette assigns a number to each pixel as its signature. Accumulating these signatures generates a final histogram-based descriptor for each silhouette, which we call a SilPH (Silhouette Poisson Histogram). For the second approach, we propose two new robust shape descriptors based on the distribution of charge density on the surface of a 3D model. The Finite Element Method is used to calculate the charge density on each triangular face of each model as a local feature. Then we utilize the Bag-of-Features and concentric sphere frameworks to perform global matching using these local features. In addition to examining the retrieval accuracy of the descriptors in comparison to the state-of-the-art approaches, the retrieval speeds as well as robustness to noise and deformation on different datasets are investigated. On the other hand, to understand new complex models, we have also utilized distribution of electrical charge for proposing a system to decompose models into meaningful parts. Our robust, efficient and fully-automatic segmentation approach is able to specify the segments attached to the main part of a model as well as locating the boundary parts of the segments. The segmentation ability of the proposed system is examined on the standard datasets and its timing and accuracy are compared with the existing state-of-the-art approaches