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

Symmetry sensitivities of Derivative-of-Gaussian filters

We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories

Learning the Irreducible Representations of Commutative Lie Groups

We present a new probabilistic model of compact commutative Lie groups that produces invariant-equivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that is used to derive the elementary particles of a system from its symmetries. Our model employs a newfound Bayesian conjugacy relation that enables fully tractable probabilistic inference over compact commutative Lie groups -- a class that includes the groups that describe the rotation and cyclic translation of images. We train the model on pairs of transformed image patches, and show that the learned invariant representation is highly effective for classification