Regularized pointwise map recovery from functional correspondence

The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases

3D shape matching and registration : a probabilistic perspective

Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

Markerless deformation capture of hoverfly wings using multiple calibrated cameras

This thesis introduces an algorithm for the automated deformation capture of hoverfly wings from multiple camera image sequences. The algorithm is capable of extracting dense surface measurements, without the aid of fiducial markers, over an arbitrary number of wingbeats of hovering flight and requires limited manual initialisation. A novel motion prediction method, called the ‘normalised stroke model’, makes use of the similarity of adjacent wing strokes to predict wing keypoint locations, which are then iteratively refined in a stereo image registration procedure. Outlier removal, wing fitting and further refinement using independently reconstructed boundary points complete the algorithm. It was tested on two hovering data sets, as well as a challenging flight manoeuvre. By comparing the 3-d positions of keypoints extracted from these surfaces with those resulting from manual identification, the accuracy of the algorithm is shown to approach that of a fully manual approach. In particular, half of the algorithm-extracted keypoints were within 0.17mm of manually identified keypoints, approximately equal to the error of the manual identification process. This algorithm is unique among purely image based flapping flight studies in the level of automation it achieves, and its generality would make it applicable to wing tracking of other insects

Non-rigid Point Set Registration with Application to Human Masticatory Muscle Deformation

Ph.DDOCTOR OF PHILOSOPH

Latent-Class Hough Forests for 3D object detection and pose estimation of rigid objects

In this thesis we propose a novel framework, Latent-Class Hough Forests, for the problem of 3D object detection and pose estimation in heavily cluttered and occluded scenes. Firstly, we adapt the state-of-the-art template-based representation, LINEMOD [34, 36], into a scale-invariant patch descriptor and integrate it into a regression forest using a novel template-based split function. In training, rather than explicitly collecting representative negative samples, our method is trained on positive samples only and we treat the class distributions at the leaf nodes as latent variables. During the inference process we iteratively update these distributions, providing accurate estimation of background clutter and foreground occlusions and thus a better detection rate. Furthermore, as a by-product, the latent class distributions can provide accurate occlusion aware segmentation masks, even in the multi-instance scenario. In addition to an existing public dataset, which contains only single-instance sequences with large amounts of clutter, we have collected a new, more challenging, dataset for multiple-instance detection containing heavy 2D and 3D clutter as well as foreground occlusions. We evaluate the Latent-Class Hough Forest on both of these datasets where we outperform state-of-the art methods.Open Acces