A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure

Efficient MRF Energy Propagation for Video Segmentation via Bilateral Filters

Segmentation of an object from a video is a challenging task in multimedia applications. Depending on the application, automatic or interactive methods are desired; however, regardless of the application type, efficient computation of video object segmentation is crucial for time-critical applications; specifically, mobile and interactive applications require near real-time efficiencies. In this paper, we address the problem of video segmentation from the perspective of efficiency. We initially redefine the problem of video object segmentation as the propagation of MRF energies along the temporal domain. For this purpose, a novel and efficient method is proposed to propagate MRF energies throughout the frames via bilateral filters without using any global texture, color or shape model. Recently presented bi-exponential filter is utilized for efficiency, whereas a novel technique is also developed to dynamically solve graph-cuts for varying, non-lattice graphs in general linear filtering scenario. These improvements are experimented for both automatic and interactive video segmentation scenarios. Moreover, in addition to the efficiency, segmentation quality is also tested both quantitatively and qualitatively. Indeed, for some challenging examples, significant time efficiency is observed without loss of segmentation quality.Comment: Multimedia, IEEE Transactions on (Volume:16, Issue: 5, Aug. 2014

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