Abstract
The map-seeking circuit algorithm (MSC) was developed by Arathorn to efficiently solve the combinatorial problem of correspondence maximization, which arises in applications like computer vision, motion estimation, image matching, and automatic speech recognition (Arathorn, D.W. in Map-Seeking Circuits in Visual Cognition: A Computational Mechanism for Biological and Machine Vision, Stanford University Press, Stanford, 2002). Given an input image, a template image, and a discrete set of transformations, the goal is to find a composition of transformations which gives the best fit between the transformed input and the template. We imbed the associated combinatorial search problem within a continuous framework by using superposition, and we analyze a resulting constrained optimization problem. We present several numerical schemes to compute local solutions, and we compare their performance on a pair of test problems: an image matching problem and the challenging problem of automatically solving a Rubik’s cube.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Angelucci, A., Levitt, B., Walton, E., Hupe, J.M., Bullier, J., Lund, J.: Circuits for local and global signal integration in the primary visual cortex. J. Neurosci. 19, 8633–8646 (2002)
Arathorn, D.W.: Recognition under transformation using ordering property of superpositions. IEE Electron. Lett. 37, 164–166 (2001)
Arathorn, D.W.: Map-Seeking Circuits in Visual Cognition: A Computational Mechanism for Biological and Machine Vision. Stanford University Press, Stanford (2002)
Arathorn, D.W.: Computation in higher visual cortices: Map-seeking circuit theory and application to machine vision. In: Proceedings of IEEE Applied Imagery Pattern Recognition Workshop, pp. 73–78 (2004)
Arathorn, D.W.: A cortically plausible inverse problem solving method applied to recognizing static and kinematic 3-D objects. In: Advances in Neural Information Processing Systems, vol. 18. MIT Press, Cambridge (2005)
Arathorn, D.W., A cortically plausible inverse problem solving method applied to complex perceptual and planning tasks. In: Proceedings SPIE Defense and Security Symposium (2006)
Calamai, P.H., Moré, J.J.: Projected gradients methods for linearly constrained problems. Math. Program. 39, 93–116 (1987)
Gedeon, T., Arathorn, D.W.: Convergence in map finding circuits, Journal of Mathematical Imaging and Vision (2007, submitted)
Joyner, D.: Adventures in Group Theory Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys. Johns Hopkins University Press, Baltimore (2002)
Moré, J.J., Toraldo, G.: On the solution of large quadratic programming problems with bound constraints. SIAM J. Optim. 1, 93–113 (1991)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)
Snider, R., Arathorn, D.W.: Terrain discovery and navigation of multi-articulated linear robot using map-seeking circuits. In: Proceedings SPIE Defence and Security Symposium (2006)
Vogel, C.R., Arathorn, D.W., Roorda, A., Parker, A.: Retinal motion estimation in adaptive optics scanning laser ophthalmoscopy. Opt. Express 14, 487–497 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Harker, S.R., Vogel, C.R. & Gedeon, T. Analysis of Constrained Optimization Variants of the Map-Seeking Circuit Algorithm. J Math Imaging Vis 29, 49–62 (2007). https://doi.org/10.1007/s10851-007-0024-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-007-0024-7