3,537,426 research outputs found
Generalised Stretched Littlewood-Richardson Coefficients
The Littlewood-Richardson (LR) coefficient counts among many other things the
LR tableaux of a given shape and a given content. We prove, that the number of
LR tableaux weakly increases if one adds to the shape and the content the shape
and the content of another LR tableau. We also investigate the behaviour of the
number of LR tableaux, if one repeatedly adds to the shape another shape with
either fixed or arbitrary content. This is a generalisation of the stretched LR
coefficients, where one repeatedly adds the same shape and content to itself.Comment: 15 pages, rewritten with more results and examples (compared with
v1), final version to appear at Journal of Combinatorial Theory
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
Statistical Model of Shape Moments with Active Contour Evolution for Shape Detection and Segmentation
This paper describes a novel method for shape representation and robust image segmentation. The proposed method combines two well known methodologies, namely, statistical shape models and active contours implemented in level set framework. The shape detection is achieved by maximizing a posterior function that consists of a prior shape probability model and image likelihood function conditioned on shapes. The statistical shape model is built as a result of a learning process based on nonparametric probability estimation in a PCA reduced feature space formed by the Legendre moments of training silhouette images. A greedy strategy is applied to optimize the proposed cost function by iteratively evolving an implicit active contour in the image space and subsequent constrained optimization of the evolved shape in the reduced shape feature space. Experimental results presented in the paper demonstrate that the proposed method, contrary to many other active contour segmentation methods, is highly resilient to severe random and structural noise that could be present in the data
- …