Matching of the Shape Function

The shape function f(k_+) describes Fermi motion effects in inclusive semi-leptonic decays such as B -> X_u+e+nu near the end-point of the lepton spectrum. We compute the leading one-loop corrections to the shape function f(k_+) in the effective theory with a hard cut-off regularization. The matching constant onto full QCD is infrared safe, i.e. the leading infrared singularity represented by the term log^2(k_+) cancels in the difference of integrals. We compare the hard cut-off result with the result in dimensional regularization, the latter containing an additional factor of two in the coefficient of the log^2(k_+) term, and consequently requiring an oversubtraction.Comment: 11 pages, 1 figure added, minor changes in the tex

Deep Shape Matching

We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps. Secondly, the network is trained with edge maps of landmark images, which are automatically obtained by a structure-from-motion pipeline. The learned representation is evaluated on a range of different tasks, providing improvements on challenging cases of domain generalization, generic sketch-based image retrieval or its fine-grained counterpart. In contrast to other methods that learn a different model per task, object category, or domain, we use the same network throughout all our experiments, achieving state-of-the-art results in multiple benchmarks.Comment: ECCV 201

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

Perceptually Motivated Shape Context Which Uses Shape Interiors

In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

Deformable Prototypes for Encoding Shape Categories in Image Databases

We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.Office of Naval Research (Young Investigator Award N00014-06-1-0661

Shape matching and clustering

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored

Efficient contour-based shape representation and matching

This paper presents an efficient method for calculating the similarity between 2D closed shape contours. The proposed algorithm is invariant to translation, scale change and rotation. It can be used for database retrieval or for detecting regions with a particular shape in video sequences. The proposed algorithm is suitable for real-time applications. In the first stage of the algorithm, an ordered sequence of contour points approximating the shapes is extracted from the input binary images. The contours are translation and scale-size normalized, and small sets of the most likely starting points for both shapes are extracted. In the second stage, the starting points from both shapes are assigned into pairs and rotation alignment is performed. The dissimilarity measure is based on the geometrical distances between corresponding contour points. A fast sub-optimal method for solving the correspondence problem between contour points from two shapes is proposed. The dissimilarity measure is calculated for each pair of starting points. The lowest dissimilarity is taken as the final dissimilarity measure between two shapes. Three different experiments are carried out using the proposed approach: letter recognition using a web camera, our own simulation of Part B of the MPEG-7 core experiment “CE-Shape1” and detection of characters in cartoon video sequences. Results indicate that the proposed dissimilarity measure is aligned with human intuition