A TABU SEARCH A TABU SEARCH APPROACH TO APPROACH TO POLYGONAL POLYGONAL

APPROXIMATION OF APPROXIMATION OF DIGITAL CURVESDIGITAL CURVES

IntroductionIntroduction• The information on digital curves is

mainly contained in the corner points which have the maximal measures of significance.

• An effective representation of digital curves not only provides compact descriptions with less memory requirement, but also facilitates feature extraction for further image analysis and pattern recognition.

IntroductionIntroduction

• An exhaustive search for the optimal polygon will result in exponential complexity.

• These sub-optimal methods fall into three categories:

(1) Sequential approaches

(2) Split-and-merge approaches(3) Dominant points detection approaches

IntroductionIntroduction• All of the sub-optimal methods are very fast

but their results may be very far away from the optimal ones.

• The optimal methods are impractical since they cost a large amount of computations.

• In this paper, we develop a more efficient near-optimal algorithm based on a tabu search technique to deal with the application.

BASIC PRINCIPLES OF BASIC PRINCIPLES OF TABU SEARCH TECHNIQUETABU SEARCH TECHNIQUE

• Tabu search (TS) is a metaheuristic method which guides a local search procedure to effectively explore the solution space of combinatorial optimization problems

• It is still very new in the field of image processing and computer vision.

• TS starts from an initial solution chosen randomly or obtained from another heuristic method, it moves iteratively from one solution to another until a certain stop criterion is satisfied.

BASIC PRINCIPLES OF BASIC PRINCIPLES OF TABU SEARCH TECHNIQUETABU SEARCH TECHNIQUE

• Those candidate moves that will lead immediately back to the recently-visited solutions are designated tabu active This process is managed by a specially designed memory mechanism, called the tabu list.

• When a move is picked in one iteration, the direction of this move is recorded in the tabu list and will not be reversed in the next iterations.

• TS is distinct from local search methods, such as the hill-climbing approach, it will not be entrapped in a local optimum.

Solution Representation and Solution Representation and Objective FunctionObjective Function

InitializationInitialization

• TS starts from an initial solution, then moves to the next best untabu solution of its neighborhood, There are two ways of generating the initial solution. One is based on randomizing, the other is based on any local search heuristic result.

Definition of MovesDefinition of Moves• We propose three types of moves：

1. A− -move (vertex deletion operation) The value of P controls the decrease rate of

the number of vertices.

2. A+ -move (vertex addition operation) The value of The objective function will

increase by one unit and become worse by performing this move.

3. B- move (vertex adjustment operation) The value of objective function will not be

changed by applying B-move since the number of vertices remains the same.

Definition Aspiration CriteriaDefinition Aspiration Criteria

• A− -move: The tabu status of an A− -move is overruled if it results in a better objective value than the best one obtained so far.

• A+ -move: The tabu status of an A+ -move is overruled if it results in an approximation error less than ε.

• B -move: The tabu status of a B-move is overruled if it results in an approximation error less than ε.

Solution Representation and Solution Representation and Objective FunctionObjective Function

• A−-move and A+-move can perturb the solution configuration and avoid being entrapped in a local optimum. B-move fine-tunes the current solution to satisfy the ε-bound constraint.

• After the best move is picked, the direction of this move is recorded in the bottom of the tabu list and should not be reversed.

The Proposed algorithm

EXPERIMENTAL RESULTS AND COMPARATIVE PERFORMANCES

The Length of the Tabu ListThe Length of the Tabu List • Longer tabu lists will force the search into areas that

were not yet visited (diversification), while shorter tabu

lists will focus on intensification.

The Number of Trial Moves

The Vertex-deletion Probability

The Vertex-deletion Probability

The Vertex-deletion Probability

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