Matching shapes using the current distance

posterCurrent Distance: It was introduced by Vaillant and Glaunès as a way of comparing shapes (point sets, curves, surfaces). This distance measure is defined by viewing a shape as a linear operator on a k-form field, and constructing a (dual) norm on the space of shapes. Shape Matching: Given two shapes P;Q, a distance measure d on shapes, and a transformation group T , the problem of shape matching is to determine a transformation T that minimizes d(P; T Q). Current Norm: For a point set P, current norm is kPk2 = X i X j K(pi; pj)) (p) (q) Current Distance: Distance between two point sets P and Q is D2(P;Q) = kP + (??1)Qk2 = kPk2 + kQk2 ?? 2 X i X j K(pi; qj)) (p) (q) It takes O(n2) time to compute the current distance between two shapes of size n. Also current distance between 2 surfaces or curves can be reduced to set of distance computations on appropriately weighted point sets

Self-prioritization and perceptual matching: The effects of temporal construal.

Recent research has revealed that self-referential processing enhances perceptual judgments - the so-called self-prioritization effect. The extent and origin of this effect remains unknown, however. Noting the multifaceted nature of the self, here we hypothesized that temporal influences on self-construal (i.e., past/future-self continuity) may serve as an important determinant of stimulus prioritization. Specifically, as representations of the self increase in abstraction as a function of temporal distance (i.e., distance from now), self-prioritization may only emerge when stimuli are associated with the current self. The results of three experiments supported this prediction. Self-relevance only enhanced performance in a standard perceptual-matching task when stimuli (i.e., geometric shapes) were connected with the current self; representations of the self in the future (Expts. 1 & 2) and past (Expt. 3) failed to facilitate decision making. To identify the processes underlying task performance, data were interrogated using a hierarchical drift diffusion model (HDDM) approach. Results of these analyses revealed that self-prioritization was underpinned by a stimulus bias (i.e., rate of information uptake). Collectively, these findings elucidate when and how self-relevance influences decisional processing

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

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

Disconnected Skeleton: Shape at its Absolute Scale

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on the stable properties of the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of the skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV: Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape Recognition. Masters thesis, Department of Computer Engineering, Middle East Technical University, May 200

Currents and finite elements as tools for shape space

The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper we study a general representation of shapes that is based on linear spaces and is suitable for numerical discretization, being robust to noise. We develop the theory of currents for shape spaces by considering both the analytic and numerical aspects of the problem. In particular, we study the analytical properties of the current map and the $H^{-s}$ norm that it induces on shapes. We determine the conditions under which the current determines the shape. We then provide a finite element discretization of the currents that is a practical computational tool for shapes. Finally, we demonstrate this approach on a variety of examples