Trees and hills: methodology for maximizing functions of systems of linear relations
Trees and hills: methodology for maximizing functions of systems of linear relations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Information Processing Letters
Robust regression and outlier detection
Robust regression and outlier detection
A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
A new curve detection method: randomized Hough transform (RHT)
Pattern Recognition Letters
A “thermal” perceptron learning rule
Neural Computation
A Hough transform algorithm with a 2D hypothesis testing kernel
CVGIP: Image Understanding
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The complexity and approximability of finding maximum feasible subsystems of linear relations
Theoretical Computer Science
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Journal of Global Optimization
Fast Heuristics for the Maximum Feasible Subsystem Problem
INFORMS Journal on Computing
A New Approach for Fast Line Detection Based on Combinatorial Optimization
ICIAP '99 Proceedings of the 10th International Conference on Image Analysis and Processing
A fast Hough transform for segment detection
IEEE Transactions on Image Processing
A two-phase relaxation-based heuristic for the maximum feasible subsystem problem
Computers and Operations Research
A greedy approach to identification of piecewise affine models
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Comparison of four procedures for the identification of hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Identification of piecewise affine systems based on statistical clustering technique
Automatica (Journal of IFAC)
Column Generation for the Minimum Hyperplanes Clustering Problem
INFORMS Journal on Computing
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We consider a new combinatorial optimization problem related to linear systems (MIN PFS) that consists, given an infeasible system, in finding a partition into a minimum number of feasible subsystems. MIN PFS allows formalization of the fundamental problem of piecewise linear model estimation, which is an attractive alternative when modeling a wide range of nonlinear phenomena. Since MIN PFS turns out to be NP-hard to approximate within every factor strictly smaller than 3/2 and we are mainly interested in real-time applications, we propose a greedy strategy based on randomized and thermal variants of the classical Agmon-Motzkin-Schoenberg relaxation method for solving systems of linear inequalities. Our method provides good approximate solutions in a short amount of time. The potential of our approach and the performance of our algorithm are demonstrated on two challenging problems from image and signal processing. The first one is that of detecting line segments in digital images and the second one that of modeling time-series using piecewise linear autoregressive models. In both cases the MIN PFS-based approach presents various advantages with respect to conventional alternatives, including wider range of applicability, lower computational requirements and no need for a priori assumptions regarding the underlying structure of the data.