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1. Ciesielski, Krzysztof Chris

et al.

Strand, Robin

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Radiology, Oncology and Radiation Science, Radiology.

Malmberg, Filip

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Radiology, Oncology and Radiation Science, Radiology.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.

This paper presents a path-based distance, where local displacement costs vary both according to the displacement vector and with the travelled distance. The corresponding distance transform algorithm is similar in its form to classical propagation-based algorithms, but the more variable distance increments are either stored in look-up-tables or computed on-the-fly. These distances and distance transform extend neighborhood-sequence distances, chamfer distances and generalized distances based on Minkowski sums. We introduce algorithms to compute a translated version of a neighborhood sequence distance map both for periodic and aperiodic sequences and a method to derive the centered distance map. A decomposition of the grid neighbors, in Z(2) and Z(3), allows to significantly decrease the number of displacement vectors needed for the distance transform. Overall, the distance transform can be computed with minimal delay, without the need to wait for the whole input image before beginning to provide the result image.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.

Ciesielski, Krzysztof Chris

Malmberg, Filip

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.

Saha, Punam K.

The minimum barrier distance2013In: Computer Vision and Image Understanding, ISSN 1077-3142, E-ISSN 1090-235X, Vol. 117, no 4, p. 429-437Article in journal (Refereed)

Abstract [en]

In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions f(A), whose domain D is a compact subsets of the Euclidean space R-n. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in R-n, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of f(A) along the path. We present several important properties of MBD, including the theorems: on the equivalence between the MBD rho(A) and its alternative definition phi(A); and on the convergence of their digital versions, (rho(A)) over cap and (phi(A)) over cap, to the continuous MBD rho(A) = phi(A) as we increase a precision of sampling. This last result provides an estimation of the discrepancy between the value of (rho(A)) over cap and of its approximation (phi(A)) over cap. An efficient computational solution for the approximation (phi(A)) over cap of (rho(A)) over cap is presented. We experimentally investigate the robustness of MBD to noise and blur, as well as its stability with respect to the change of a position of points within the same object (or its background). These experiments are used to compare MBD with other distance functions: fuzzy distance, geodesic distance, and max-arc distance. A favorable outcome for MBD of this comparison suggests that the proposed minimum barrier distance is potentially useful in different imaging tasks, such as image segmentation.