Sibel Tari

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 stable properties the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of the 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 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.

Dissimilarity between two skeletal trees in a context

Skeletal trees are commonly used in order to express geometric properties of the shape. Accordingly, tree-edit distance is used to compute a dissimilarity between two given shapes. We present a new tree-edit based shape matching method which uses a recent coarse skeleton representation. The coarse skeleton representation allows us to represent both shapes and shape categories in the form of depth-1 trees. Consequently, we can easily integrate the influence of the categories into shape dissimilarity measurements. The new dissimilarity measure gives a better within group versus between group separation, and it mimics the asymmetric nature of human similarity judgements.

Mumford-Shah regularizer with contextual feedback

We present a simple and robust feature preserving image regularization by letting local region measures modulate the diffusivity. The purpose of this modulation is to disambiguate low level cues in early 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 both gray and color natural images demonstrate the potential of the method under difficult noise types, non-uniform contrast, existence of multi-scale patterns and textures.

Hierarchical Shape Decomposition via Level Sets

A new tool for shape decomposition is presented. It is a function defined on the shape domain and computed using a linear system of equations. It is demonstrated that the level curves of the new function provide a hierarchical partitioning of the shape domain into visual parts, without requiring any features to be estimated. The new tool is an unconventional distance transform where the minimum distance to the union of the shape boundary and an unknown critical curve is computed. This curve divides the shape domain into two parts, one corresponding to the coarse scale structure and the other one corresponding to the fine scale structure. The connection of the new function to a variety of morphological concepts (Skeleton by Influence Zone, Aslan Skeleton, and Weighted Distance Transforms) is discussed.

A similarity-based approach for shape classification using Aslan skeletons

Shape skeletons are commonly used in generic shape recognition as they capture part hierarchy, providing a structural representation of shapes. However, their potential for shape classification has not been investigated much. In this study, we present a similarity-based approach for classifying 2D shapes based on their Aslan skeletons (Aslan and Tari, 2005; Aslan et al., 2008). The coarse structure of this skeleton representation allows us to represent each shape category in the form of a reduced set of prototypical trees, offering an alternative solution to the problem of selecting the best representative examples. The ensemble of these category prototypes is then used to form a similarity-based representation space in which the similarities between a given shape and the prototypes are computed using a tree edit distance algorithm, and support vector machine (SVM) classifiers are used to predict the category membership of the shape based on computed similarities.

Embedding Shapes without Predefined Parts

For a practical computer implementation of part embedding in shapes that is also true to their continuous character and the shape grammar formalism, shapes and their boundaries are handled together in composite shape and label algebras. Temporary representations of shapes, termed ‘overcomplete graphs’, comprise boundary elements of shapes and how they are assembled, and are utilized in a two-phase algorithm that systematically searches for embedded parts. The associated implementation is developed to receive user-defined constraints for an interactive search. In particular, the user-defined reference shape extends the search to nondeterministic cases.

Landmarks inside the shape

In the last few decades, significant advances in image matching are provided by rich local descriptors that are defined through physical measurements such as reflectance. As such measurements are not naturally available for silhouettes, existing arsenal of image matching tools cannot be utilized in shape matching. We propose that the recently presented SPEM representation can be used analogous to image intensities to detect local keypoints using invariant image salient point detectors. We devise a shape similarity measure based on the number of matching internal regions. The performance of the similarity measure in planar shape retrieval indicates that the landmarks inside the shape silhouettes provide a strong representation of the regional characteristics of 2D planar shapes. Graphical abstractDisplay Omitted HighlightsAn internal-landmark based planar shape matching scheme is proposed.The shape landmarks are obtained using the recently proposed SPEM representation.Properties of SPEM that allow the use of image descriptors inside shapes are discussed.Statistical evidence indicates that the number of matches can be used as a similarity measure.

Weighted shapes for embedding perceived wholes

Embedding parts is a key problem in computing when dealing with continuous matter such as shapes rather than discrete matter such as symbols. For computing part relations such as embedding, a technical framework that uses weighted shapes is introduced and implemented. In the proposed framework, for any given two-dimensional shape, the entire canvas is defined as a weighted shape and serves as a registration mark in detecting embedded parts. The approach treats shapes as perceived wholes rather than composed and eliminates the technical distinction between shape categories such as line, curve, or plane. The implementation is shown for two-dimensional shapes but is extendable to three dimensions. As demonstrated on a Seljuk geometric pattern, the framework allows for embedding multiple and various perceived wholes, thus exploring emerging shapes and shape relations to be used for analysis and synthesis in design.

From a modified ambrosio-tortorelli to a randomized part hierarchy tree

We demonstrate the possibility of coding parts, features that are higher level than boundaries, using a modified AT field after augmenting the interaction term of the AT energy with a non-local term and weakening the separation into boundary/not-boundary phases. The iteratively extracted parts using the level curves with double point singularities are organized as a proper binary tree. Inconsistencies due to non-generic configurations for level curves as well as due to visual changes such as occlusion are successfully handled once the tree is endowed with a probabilistic structure. The work is a step in establishing the AT function as a bridge between low and high level visual processing.

Minimally Stochastic Schemes for Singular Diffusion Equations

Total variation (TV) and balanced forward-backward (BFB) diffusion are prominent examples of singular diffusion equations: Finite extinction time, the experimentally observed tendency to create piecewise constant regions, and being free of parameters makes them very interesting. However, their appropriate numerical treatment is still a challenge. In this paper a minimally stochastic approach to these singular equations is presented. It is based on analytical solutions of two-pixel signals and stochastic rounding. This introduces regularisation via integer arithmetic and does not require any limits on the diffusivity. Experiments demonstrate the favourable performance of the proposed probabilistic method.