Fast Adaptive Reparametrization (FAR) with Application to Human Action Recognition

In this paper, a fast approach for curve reparametrization, called Fast Adaptive Reparamterization (FAR), is introduced. Instead of computing an optimal matching between two curves such as Dynamic Time Warping (DTW) and elastic distance-based approaches, our method is applied to each curve independently, leading to linear computational complexity. It is based on a simple replacement of the curve parameter by a variable invariant under specific variations of reparametrization. The choice of this variable is heuristically made according to the application of interest. In addition to being fast, the proposed reparametrization can be applied not only to curves observed in Euclidean spaces but also to feature curves living in Riemannian spaces. To validate our approach, we apply it to the scenario of human action recognition using curves living in the Riemannian product Special Euclidean space SE(3) n. The obtained results on three benchmarks for human action recognition (MSRAction3D, Florence3D, and UTKinect) show that our approach competes with state-of-the-art methods in terms of accuracy and computational cost

Part-based recognition of 3-D objects with application to shape modeling in hearing aid manufacturing

In order to meet the needs of people with hearing loss today hearing aids are custom designed. Increasingly accurate 3-D scanning technology has contributed to the transition from conventional production scenarios to software based processes. Nonetheless, there is a tremendous amount of manual work involved to transform an input 3-D surface mesh of the outer ear into a final hearing aid shape. This manual work is often cumbersome and requires lots of experience which is why automatic solutions are of high practical relevance. This work is concerned with the recognition of 3-D surface meshes of ear implants. In particular we present a semantic part-labeling framework which significantly outperforms existing approaches for this task. We make at least three contributions which may also be found useful for other classes of 3-D meshes. Firstly, we validate the discriminative performance of several local descriptors and show that the majority of them performs poorly on our data except for 3-D shape contexts. The reason for this is that many local descriptor schemas are not rich enough to capture subtle variations in form of bends which is typical for organic shapes. Secondly, based on the observation that the left and the right outer ear of an individual look very similar we raised the question how similar the ear shapes among arbitrary individuals are? In this work, we define a notion of distance between ear shapes as building block of a non-parametric shape model of the ear to better handle the anatomical variability in ear implant labeling. Thirdly, we introduce a conditional random field model with a variety of label priors to facilitate the semantic part-labeling of 3-D meshes of ear implants. In particular we introduce the concept of a global parametric transition prior to enforce transition boundaries between adjacent object parts with an a priori known parametric form. In this way we were able to overcome the issue of inadequate geometric cues (e.g., ridges, bumps, concavities) as natural indicators for the presence of part boundaries. The last part of this work offers an outlook to possible extensions of our methods, in particular the development of 3-D descriptors that are fast to compute whilst at the same time rich enough to capture the characteristic differences between objects residing in the same class

Geometric Approaches for 3D Shape Denoising and Retrieval

A key issue in developing an accurate 3D shape recognition system is to design an efficient shape descriptor for which an index can be built, and similarity queries can be answered efficiently. While the overwhelming majority of prior work on 3D shape analysis has concentrated primarily on rigid shape retrieval, many real objects such as articulated motions of humans are nonrigid and hence can exhibit a variety of poses and deformations. Motivated by the recent surge of interest in content-based analysis of 3D objects in computeraided design and multimedia computing, we develop in this thesis a unified theoretical and computational framework for 3D shape denoising and retrieval by incorporating insights gained from algebraic graph theory and spectral geometry. We first present a regularized kernel diffusion for 3D shape denoising by solving partial differential equations in the weighted graph-theoretic framework. Then, we introduce a computationally fast approach for surface denoising using the vertexcentered finite volume method coupled with the mesh covariance fractional anisotropy. Additionally, we propose a spectral-geometric shape skeleton for 3D object recognition based on the second eigenfunction of the Laplace-Beltrami operator in a bid to capture the global and local geometry of 3D shapes. To further enhance the 3D shape retrieval accuracy, we introduce a graph matching approach by assigning geometric features to each endpoint of the shape skeleton. Extensive experiments are carried out on two 3D shape benchmarks to assess the performance of the proposed shape retrieval framework in comparison with state-of-the-art methods. The experimental results show that the proposed shape descriptor delivers best-in-class shape retrieval performance

Geometric Deep Learned Descriptors for 3D Shape Recognition

The availability of large 3D shape benchmarks has sparked a flurry of research activity in the development of efficient techniques for 3D shape recognition, which is a fundamental problem in a variety of domains such as pattern recognition, computer vision, and geometry processing. A key element in virtually any shape recognition method is to represent a 3D shape by a concise and compact shape descriptor aimed at facilitating the recognition tasks. The recent trend in shape recognition is geared toward using deep neural networks to learn features at various levels of abstraction, and has been driven, in large part, by a combination of affordable computing hardware, open source software, and the availability of large-scale datasets. In this thesis, we propose deep learning approaches to 3D shape classification and retrieval. Our approaches inherit many useful properties from the geodesic distance, most notably the capture of the intrinsic geometric structure of 3D shapes and the invariance to isometric deformations. More specifically, we present an integrated framework for 3D shape classification that extracts discriminative geometric shape descriptors with geodesic moments. Further, we introduce a geometric framework for unsupervised 3D shape retrieval using geodesic moments and stacked sparse autoencoders. The key idea is to learn deep shape representations in an unsupervised manner. Such discriminative shape descriptors can then be used to compute pairwise dissimilarities between shapes in a dataset, and to find the retrieved set of the most relevant shapes to a given shape query. Experimental evaluation on three standard 3D shape benchmarks demonstrate the competitive performance of our approach in comparison with existing techniques. We also introduce a deep similarity network fusion framework for 3D shape classification using a graph convolutional neural network, which is an efficient and scalable deep learning model for graph-structured data. The proposed approach coalesces the geometrical discriminative power of geodesic moments and similarity network fusion in an effort to design a simple, yet discriminative shape descriptor. This geometric shape descriptor is then fed into the graph convolutional neural network to learn a deep feature representation of a 3D shape. We validate our method on ModelNet shape benchmarks, demonstrating that the proposed framework yields significant performance gains compared to state-of-the-art approaches

Medical Image Registration and 3D Object Matching

The great challenge in image registration and 3D object matching is to devise computationally efficient algorithms for aligning images so that their details overlap accurately and retrieving similar shapes from large databases of 3D models. The first problem addressed is this thesis is medical image registration, which we formulate as an optimization problem in the information-theoretic framework. We introduce a viable and practical image registration method by maximizing an entropic divergence measure using a modified simultaneous perturbation stochastic approximation algorithm. The feasibility of the proposed image registration approach is demonstrated through extensive experiments. The rest of the thesis is devoted to a joint exploitation of geometry and topology of 3D objects for as parsimonious as possible representation of models and its subsequent application in 3D object representation, matching, and retrieval problems. More precisely, we introduce a skeletal graph for topological 3D shape representation using Morse theory. The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function. We also propose a novel graph matching algorithm by comparing the relative shortest paths between the skeleton endpoints. Moreover, we describe a skeletal graph for 3D object matching and retrieval. This skeleton is constructed from the second eigenfunction of the Laplace-Beltrami operator defined on the surface of the 3D object. Using the generalized eigenvalue decomposition, a matrix computational framework based on the finite element method is presented to compute the spectrum of the Laplace-Beltrami operator. Illustrating experiments on two standard 3D shape benchmarks are provided to demonstrate the feasibility and the much improved performance of the proposed skeletal graphs as shape descriptors for 3D object matching and retrieval

Deformation Based Curved Shape Representation

Representation and modelling of an objects' shape is critical in object recognition, synthesis, tracking and many other applications in computer vision. As a result, there is a wide range of approaches in formulating representation space and quantifying the notion of similarity between shapes. A similarity metric between shapes is a basic building block in modelling shape categories, optimizing shape valued functionals, and designing a classifier. Consequently, any subsequent shape based computation is fundamentally dependent on the computational efficiency, robustness, and invariance to shape preserving transformations of the defined similarity metric. In this thesis, we propose a novel finite dimensional shape representation framework that leads to a computationally efficient, closed form solution, and noise tolerant similarity distance function. Several important characteristics of the proposed curved shape representation approach are discussed in relation to earlier works. Subsequently, two different solutions are proposed for optimal parameter estimation of curved shapes. Hence, providing two possible solutions for the point correspondence estimation problem between two curved shapes. Later in the thesis, we show that several statistical models can readily be adapted to the proposed shape representation framework for object category modelling. The thesis finalizes by exploring potential applications of the proposed curved shape representation in 3D facial surface and facial expression representation and modelling