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The human visual system samples at many scales at the same time. This inspired Witkin and Koenderink [1, 2] and later on many other image processing researchers to start working on scale-space theory. The notion of scale is made explicit by studying the deep structure of images. Quoting Koenderink in his 1984 article on scale-space theory: “Study the family as a family, i.e. define deep structure, the relation between structural features of different derived images.” A hierarchical structure hidden inside the deep structure of an image can be described by studying its special singularities called toppoints. Toppoints provide a natural way of incorporating scale into image processing algorithms. This leads to algorithms that are of a multiscale nature by definition, which often results in superior performance compared to its single-scale counterparts. Application areas include, matching, object retrieval, coding, optic flow estimation, segmentation and others.
In order to study information content of the toppoints we developed a linear reconstruction method that aims to recover the original image from its toppoints. This involves heavy linear algebra and benefits from a symbolic definition of the problem. These requirements make Mathematica a natural candidate for the implementation of our algorithm. We show the application of MathLink and the Parallel Computing Toolkit, taking advantage of the giganumeric capabilities of Mathematica in the demanding setting of our reconstruction problem.
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