The Map Seeking Circuit (MSC) has been suggested to address the inverse problem of transformation discovery as found in signal processing, vision, inverse kinematics and many other natural tasks. According to this idea, a parallel search in the transformation space of a high dimensional problem can be decomposed into parts efficiently using the ordering property of superpositions. Deterministic formulations of the circuit have been suggested. Here, we provide a probabilistic interpretation of the architecture whereby the superpositions of the circuit are seen as a series of marginalisations over parameters of the transform. Based on this, we interpret the weights of the MSC as importance weights. The latter suggests the incorporation of Monte-Carlo approaches in the MSC, providing improved resolution of parameter estimates within resource constrained implementations. As a final contribution, we model mixed serial/parallel search strategies of biological vision to reduce the problem of collusions, a common problem in the standard MSC approach.

The steering framework significantly reduces the computational cost of detecting and extracting oriented low-level spatial features in images by linearly combining the responses of a small set of basis filters at fixed orientations to yield filter responses at arbitrary orientations. However, the characteristics of the steered filter, such as orientation and scale selectivity, remain the same as those of the basis filters. We show that linear combination with the appropriate basis filters and weights can achieve more. We present a novel approach for sharpening the orientation selectivity of polar-separable filters by linear combination and well-known trigonometric identities which reduces the need for more basis filters with higher orientation selectivity. We describe the principles for and issues with designing quadrature sharpening filters. We also qualitatively and quantitatively compare 4-basis sharpened filter kernels with an equivalent steerable set of 6-basis filters

The dominant orientation at any point, P, in an image is the direction from P in which there is the least gray-level variance. It is often defined by using gradient estimates, but may be extended to employ neighbourhood operators that provide some degree of phase invariance. However, the approach to estimating the dominant orientation at P depends on the scale or size of the (usually) non-trivial neighbourhood being considered. Multiscale PCA-based orientation estimation techniques involve computationally-heavy solving of eigensystems at each scale and location. In contrast, we propose two methods which use a measure of anisotropy to select or weight orientations respectively at different scales in order to provide a single estimate of orientation at any given point. This is believed to be closer to human perception of contour direction. Results are presented for two simple orientation estimation techniques against comparisons with multiscale PCA estimation for human perceptual boundaries.

This work addresses the design of a novel complex steerable wavelet construction, the generation of transform-space feature measurements associated with corner and edge presence and orientation properties, and the application of these measurements directly to image denoising. The decomposition uses pairs of bandpass filters that display symmetry and antisymmetry about a steerable axis of orientation. While the angular characterization of the bandpass filters is similar to those previously described, the radial characteristic is new, as is the manner of constructing the interpolation functions for steering. The complex filters have been engineered into a multirate system, providing a synthesis and analysis subband filtering system with good reconstruction properties. Although the performance of our proposed denoising strategy is currently below that of recently reported state-of-the-art techniques in denoising, it does compare favorably with wavelet coring approaches employing global thresholds and with an "Oracle" shrinkage technique, and presents a very promising avenue for exploring structure-based denoising in the wavelet domain.

Visual interpretation of events requires both an appropriate representation of change occurring in the scene and the application of semantics for differentiating between different types of change. Conventional approaches for tracking objects and modelling object dynamics make use of either temporal region-correlation or pre-learnt shape or appearance models. We propose a new pixel-level approach for learning the temporal characteristics of change at individual pixels. Gaussian mixture models are used to model slow long-term changes in pixel distributions while pixel energy histories are used to extract fast-change signatures from short-term events and modelled by CONDENSATION matching.