Deformable kernels for early vision

Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of `basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed

Principled Design and Implementation of Steerable Detectors

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown position and orientation. We propose a continuous-domain additive image model, where the analyzed image is the sum of the template and an isotropic background signal with self-similar isotropic power-spectrum. The method is able to learn an optimal steerable filter fulfilling the SNR criterion based on one single template and background pair, that therefore strongly responds to the template, while optimally decoupling from the background model. The proposed filter then allows for a fast detection process, with the unknown orientation estimation through the use of steerability properties. In practice, the implementation requires to discretize the continuous-domain formulation on polar grids, which is performed using radial B-splines. We demonstrate the practical usefulness of our method on a variety of template approximation and pattern detection experiments

Deformable kernels for early vision

Early vision algorithms often have a first stage of linear filtering that 'extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. This discretization produces anisotropies due to a loss of traslation-, rotation- scaling- invariance that makes early vision algorithms less precise and more difficult to design. This need not be so: one can compute and store efficiently the response of families of linear filters defined on a continuum of orientations and scales. A technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of a small number of 'basis' functions; (2) to describe all finite-dimensional families, i.e. the families of filters for which a finite dimensional representation is possible with no error. The technique is general and can be applied to generating filters in arbitrary dimensions. Experimental results are presented that demonstrate the applicability of the technique to generating multi-orientation multi-scale 20 edge-detection kernels. The implementation issues are also discussed

Segmentation of Sedimentary Grain in Electron Microscopy Image

This paper describes a novel method developed for the segmentation of sedimentary grains in electron microscopy images. The algorithm utilizes the approach of region splitting and merging. In the splitting stage, the marker-based watershed segmentation is used. In the merging phase, the typical characteristics of grains in electron microscopy images are exploited for proposing special metrics, which are then used during the merging stage to obtain a correct grain segmentation. The metrics are based on the typical intensity changes on the grain borders and the compact shape of grains. The experimental part describes the optimal setting of parameter in the splitting stage and the overall results of the proposed algorithm tested on available database of grains. The results show that the proposed technique fulfills the requirements of its intended application

Deformable kernels for early vision

Caption title.Includes bibliographical references (p. 22-24).Research supported by the U.S. Army Research Office. DAAL01-86-K-0171Pietro Perona