We present a simple and robust feature preserving image regularization by letting local region measures to modulate the diffusivity. The purpose of this modulation is to disambiguate low level cues in early both gray and color natural images demonstrate the potential of the method under difficult noise types, nonuniform contrast, existence of multi-scale patterns and textures. Key words variational and PDE methods, feature preserving diffusion, structure preserving diffusion, disambiguation in low level vision. vision. We interpret the Ambrosio-Tortorelli approximation of the Mumford-Shah model as a system with modulatory feedback and utilize this interpretation to integrate high level information into the regularization process. The method does not require any prior model or learning; the high level information is extracted from local regions and fed back to the regularization step. An important characteristic of the method is that both negative and positive feedback can be simultaneously used without creating oscillations. Experiments performed with

Abstract. Local symmetry axis based schemes have been used for generic shape recognition as they lead to articulation insensitive representations. Despite their strengths, purely syntactic level of axial representations precludes the possibility of distinguishing a likely articulation from an unlikely one. In order to overcome this weakness, syntax should be combined with pragmatics and/or semantics. As a solution we propose a novel articulation space which enables inferences on the likelihood of possible articulations. Articulation priors can be constructed directly from examples (pragmatics) or set externally (semantics). We incorporate articulation priors to a skeletal matching scheme to arrive at an enriched axial representation which is sensitive to unlikely articulations but insensitive to likely ones. 2 1

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.

Representing a 3D shape by a set of one-dimensional curves that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several machine intelligence tasks. This paper presents a fast, automatic, and robust variational framework for computing continuous, sub-voxel accurate curve skeletons from volumetric objects. A reference point inside the object is considered a point source that transmits two wave fronts of different energies. The first front (β-front) converts the object into a graph, from which the object salient topological nodes are determined. Curve skeletons are tracked from those nodes along the cost field constructed by the second front (α-front) until the point source is reached. The accuracy and robustness of the proposed work are validated against competing techniques as well as a database of 3D objects. Unlike other state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying skeletal junction nodes, employs a new energy that does not form medial surfaces, and finally extracts curve skeletons that correspond to the most prominent parts of the shape, and are hence less sensitive to noise.

from skeletal shape trees

• Compute the local symmetries only at the locations where it can be accurately determined. • Select a shape dependent scale σ * in which its representation is most stable. Disconnected Skeleton • Construct the distance surface ø as the solution of the following linear diffusion equation at a special scale σ*: (1) • Related to the edge strength function v used in

In this paper, we propose a new definition of curvature, called visual curvature. It is based on statistics of the extreme points of the height functions computed over all directions. By gradually ignoring relatively small heights, a multi-scale curvature is obtained. The theoretical properties and the experiments presented demonstrate that multi-scale visual curvature is stable, even in the presence of significant noise. To our best knowledge, the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves. Moreover, it yields stable curvature estimates of curves in digital images even under sever distortions. We also show a relation between multi-scale visual curvature and convexity of simple closed curves.

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