Fast adaptive elliptical filtering using box splines

We demonstrate that it is possible to filter an image with an elliptic window of varying size, elongation and orientation with a fixed computational cost per pixel. Our method involves the application of a suitable global pre-integrator followed by a pointwise-adaptive localization mesh. We present the basic theory for the 1D case using a B-spline formalism and then appropriately extend it to 2D using radially-uniform box splines. The size and ellipticity of these radially-uniform box splines is adaptively controlled. Moreover, they converge to Gaussians as the order increases. Finally, we present a fast and practical directional filtering algorithm that has the capability of adapting to the local image features.Comment: 9 pages, 1 figur

Fast space-variant elliptical filtering using box splines

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based on a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using pre-integration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based on the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.Comment: 12 figures; IEEE Transactions on Image Processing, vol. 19, 201

Framework to Enhance Teaching and Learning in System Analysis and Unified Modelling Language

Cowling, MA ORCiD: 0000-0003-1444-1563; Munoz Carpio, JC ORCiD: 0000-0003-0251-5510Systems Analysis modelling is considered foundational for Information and Communication Technology (ICT) students, with introductory and advanced units included in nearly all ICT and computer science degrees. Yet despite this, novice systems analysts (learners) find modelling and systems thinking quite difficult to learn and master. This makes the process of teaching the fundamentals frustrating and time intensive. This paper will discuss the foundational problems that learners face when learning Systems Analysis modelling. Through a systematic literature review, a framework will be proposed based on the key problems that novice learners experience. In this proposed framework, a sequence of activities has been developed to facilitate understanding of the requirements, solutions and incremental modelling. An example is provided illustrating how the framework could be used to incorporate visualization and gaming elements into a Systems Analysis classroom; therefore, improving motivation and learning. Through this work, a greater understanding of the approach to teaching modelling within the computer science classroom will be provided, as well as a framework to guide future teaching activities