8,407 research outputs found
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
A model-based approach to recovering the structure of a plant from images
We present a method for recovering the structure of a plant directly from a
small set of widely-spaced images. Structure recovery is more complex than
shape estimation, but the resulting structure estimate is more closely related
to phenotype than is a 3D geometric model. The method we propose is applicable
to a wide variety of plants, but is demonstrated on wheat. Wheat is made up of
thin elements with few identifiable features, making it difficult to analyse
using standard feature matching techniques. Our method instead analyses the
structure of plants using only their silhouettes. We employ a generate-and-test
method, using a database of manually modelled leaves and a model for their
composition to synthesise plausible plant structures which are evaluated
against the images. The method is capable of efficiently recovering accurate
estimates of plant structure in a wide variety of imaging scenarios, with no
manual intervention
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
Deep Learning on Lie Groups for Skeleton-based Action Recognition
In recent years, skeleton-based action recognition has become a popular 3D
classification problem. State-of-the-art methods typically first represent each
motion sequence as a high-dimensional trajectory on a Lie group with an
additional dynamic time warping, and then shallowly learn favorable Lie group
features. In this paper we incorporate the Lie group structure into a deep
network architecture to learn more appropriate Lie group features for 3D action
recognition. Within the network structure, we design rotation mapping layers to
transform the input Lie group features into desirable ones, which are aligned
better in the temporal domain. To reduce the high feature dimensionality, the
architecture is equipped with rotation pooling layers for the elements on the
Lie group. Furthermore, we propose a logarithm mapping layer to map the
resulting manifold data into a tangent space that facilitates the application
of regular output layers for the final classification. Evaluations of the
proposed network for standard 3D human action recognition datasets clearly
demonstrate its superiority over existing shallow Lie group feature learning
methods as well as most conventional deep learning methods.Comment: Accepted to CVPR 201
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