In this paper, we present feature/detail preserving models for color image smoothing and segmentation using the Hamiltonian quaternion framework. First, we introduce a novel quaternionic Gabor filter (QGF) which can combine the color channels and the orientations in the image plane. We show that these filters are optimally localized both in the spatial and frequency domains and provide a good approximation to quaternionic quadrature filters. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose continuous mixtures of appropriate exponential basis functions and derive analytic expressions for these models. These analytic expressions take the form of spatially varying kernels which, when convolved with a color image or the signed distance function of an evolving contour (placed in the color image), yield a detail preserving smoothing and segmentation, respectively. Several examples on widely used image databases are shown to depict the performance of our algorithms.

Many computer vision and image processing tasks require the preservation of local discontinuities, terminations and bifurcations. Denoising with feature preservation is a challenging task and in this paper, we present a novel technique for preserving complex oriented structures such as junctions and corners present in images. This is achieved in a two stage process namely, (1) All image data are pre-processed to extract local orientation information using a steerable Gabor filter bank. The orientation distribution at each lattice point is then represented by a continuous mixture of Gaussians. The continuous mixture representation can be cast as the Laplace transform of the mixing density over the space of positive definite (covariance) matrices. This mixing density is assumed to be a parameterized distribution, namely, a mixture of Wisharts whose Laplace transform is evaluated in a closed form expression called the Rigaut type function, a scalar-valued function of the parameters of the Wishart distribution. Computation of the weights in the mixture Wisharts is formulated as a sparse deconvolution problem. (2) The feature preserving denoising is then achieved via iterative convolution of the given image data with the Rigaut type function. We present experimental results on noisy data, real 2D images and 3D MRI data acquired from plant roots depicting bifurcating roots. Superior performance of our technique is depicted via comparison to the state-of-the-art anisotropic diffusion filter.

In-memory nearest neighbor computation is a typical collaborative filtering approach for high recommendation accuracy. However, this approach is not scalable given the huge number of customers and items in typical commercial applications. Cluster-based collaborative filtering techniques can be a remedy for the efficiency problem, but they usually provide relatively lower accuracy figures, since they may become over-generalized and produce less-personalized recommendations. Our research explores an individualistic strategy which initially clusters the users and then exploits the members within clusters, but not just the cluster representatives, during the recommendation generation stage. We provide an efficient implementation of this strategy by adapting a specifically tailored cluster- skipping inverted index structure. Experimental results reveal that the individualistic strategy with the cluster-skipping index is a good compromise that yields high accuracy and reasonable scalability figures. © 2012 Elsevier Ltd. All rights reserved

Image segmentation is a fundamental task in Computer Vision and there are numerous algorithms that have been successfully applied in various domains. There are still plenty of challenges to be met with. In this paper, we consider one such challenge, that of achieving segmentation while preserving complicated and detailed features present in the image, be it a gray level or a textured image. We present a novel approach that does not make use of any prior information about the objects in the image being segmented. Segmentation is achieved using local orientation information, which is obtained via the application of a steerable Gabor filter bank, in a statistical framework. This information is used to construct a spatially varying kernel called the Rigaut Kernel, which is then convolved with the signed distance function of an evolving contour (placed in the image) to achieve segmentation. We present numerous experimental results on real images, including a quantitative evaluation. Superior performance of our technique is depicted via comparison to the state-of-the-art algorithms in literature.

In this paper, we present a feature/detail preserving color image segmentation framework using Hamiltonian quaternions. First, we introduce a novel Quaternionic Gabor Filter (QGF) which can combine the color channels and the orientations in the image plane. Using the QGFs, we extract the local orientation information in the color images. Second, in order to model this derived orientation information, we propose a continuous mixture of appropriate hypercomplex exponential basis functions. We derive a closed form solution for this continuous mixture model. This analytic solution is in the form of a spatially varying kernel which, when convolved with the signed distance function of an evolving contour (placed in the color image), yields a detail preserving segmentation.