Abstract
Estimation of parameters from image tokens is a central problem in computer vision. FNS, CFNS and HEIV are three recently developed methods for solving special but important cases of this problem. The schemes are means for finding unconstrained (FNS, HEIV) and constrained (CFNS) minimisers of cost functions. In earlier work of the authors, FNS, CFNS and a core version of HEIV were applied to a specific cost function. Here we extend the approach to more general cost functions. This allows the FNS, CFNS and HEIV methods to be placed within a common framework.
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Wojciech Chojnacki is a professor of mathematics in the Department of Mathematics and Natural Sciences at Cardinal Stefan Wyszyński University in Warsaw. He is concurrently a senior research fellow in the School of Computer Science at the University of Adelaide working on a range of problems in computer vision. His research interests include differential equations, mathematical foundations of computer vision, functional analysis, and harmonic analysis. He is author of over 70 articles on pure mathematics and machine vision, and a member of the Polish Mathematical Society.
Michael J. Brooks holds the Chair in Artificial Intelligence within the University of Adelaide’s School of Computer Science, which he heads. He is also leader of the Image Analysis Program within the Cooperative Research Centre for Sensor Signal and Information Processing, based in South Australia. His research interests include structure from motion, self-calibration, metrology, statistical vision-parameter estimation, and video surveillance and analysis. He is author of over 100 articles on vision, actively involved in a variety of commercial applications, an Associate Editor of the International Journal of Computer Vision, and a Fellow of the Australian Computer Society.
Anton van den Hengel is a senior lecturer in the School of Computer Science within the University of Adelaide. He is also leader of the Video Surveillance and Analysis Project within the Cooperative Research Centre for Sensor Signal and Information Processing. His research interests include structure from motion, parameter estimation theory, and commercial applications of computer vision.
Darren Gawley graduated with first class honours from the School of Computer Science at the University of Adelaide. He holds a temporary lectureship at the same University, and is currently finalising his PhD in the field of computer vision.
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Chojnacki, W., Brooks, M.J., van den Hengel, A. et al. FNS, CFNS and HEIV: A Unifying Approach. J Math Imaging Vis 23, 175–183 (2005). https://doi.org/10.1007/s10851-005-6465-y
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DOI: https://doi.org/10.1007/s10851-005-6465-y