Optimal extended optical flow subject to a statistical constraint

• Published in: Journal of computational and applied mathematics Vol. 234; no. 4; pp. 1291 - 1302
• Main Authors: Clarysse, Patrick, Delhay, Bertrand, Picq, Martine, Pousin, Jérôme
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 15.06.2010; Elsevier
• Subjects: Computer Science; Engineering Sciences; Exact sciences and technology; Image Processing; Mathematical analysis; Mathematics; Medical Imaging; Modeling and Simulation; Numerical Analysis; Numerical analysis. Scientific computation; Parzen approximation; Sciences and techniques of general use; Set of nonconvex constraints; Signal and Image processing; Tangency condition; Transport equation; Viability; 65C20; 35L85; Tangency condition; Transport equation; 62P10; Parzen approximation; 35F40; Set of nonconvex constraints; 35R05; Viability; Approximation; Implementation; Transport process; Numerical analysis; Sufficient condition; Applied mathematics; Optimal flow
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2009.10.014

This work is motivated by the necessity to improve heart image tracking. This technique is related to the ability of generating an apparent continuous motion, which is observable through the variation of intensity from a starting image to an ending one. Given two images ρ 0 and ρ 1 , we calculate an evolution process ρ ( t , ⋅ ) which transports ρ 0 to ρ 1 by using the optimal extended optical flow. Such a strategy is found to be well suited for heart image tracking, provided the motion is controlled by a statistical model. In this paper we use viability theory to give sufficient conditions to handle the optimal extended optical flow subject to a point-wise statistical constraint by using Parzen’s approximation. The strategy is implemented in a 1D case and the numerical results which are presented show the efficiency of the proposed strategy.