MIT16_410F10_lec05

MIT16_410F10_lec05 - Constraint Programming: Modeling, Arc...

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1 Constraint Programming: Modeling, Arc Consistency and Propagation 1 Brian C. Williams 16.410-13 September 22 nd , 2010 Slides draw material from: 6.034 notes, by Tomas Lozano Perez Constraint Processing, by Rina Dechter Brian Williams, Fall 10 Brian Williams, Fall 10 2 Assignments • Assignment: • Problem Set #2 due today, Wed. Sept. 22 nd , 2010. • Problem Set #3: Analysis, Path Planning and Constraint Programming, out today, due Wed., Sept. 29 th , 2010. • Reading: • Today: [AIMA] Ch. 6.1, 24.3-5; Constraint Modeling. • Monday: [AIMA] Ch. 6.2-5; Constraint Satisfaction. • To Learn More: Constraint Processing , by Rina Dechter – Ch. 2: Constraint Networks – Ch. 3: Consistency Enforcing and Propagation
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Outline Interpreting line diagrams Constraint satisfaction problems (CSP) [aka constraint programs (CP)]. Solving CSPs Case study: Scheduling (Appendix) Brian Williams, Fall 10 3 Outline Interpreting line diagrams Constraint modeling Constraint propagation Constraint satisfaction problems (CSP) aka constraint programs (CP) Solving CSPs Case study: Scheduling (Appendix) Brian Williams, Fall 10 4 2
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5 Labeling Line Diagrams for Visual Interpretation Input: Line drawing (a graph) Physical constraints Output: Consistent assignment of line (edge) types depth discontinuity surface orientation discontinuity reflectance discontinuity Huffman Clowes (1971): Interpret opaque, trihedral solids Step 1: Label line types. + + + + Convex Edge + Concave Edge Brian Williams, Fall 10 Requirement: Labeling must extend to complex objects Brian Williams, Fall 10 6 3
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7 Line Labeling as Constraint Programming depth discontinuity surface orientation discontinuity Huffman Clowes (1971): Interpretation of opaque, trihedral solids with no surface marks. 18 vertex labelings that are physically realizable + + + + Convex Edge + Concave Edge + + + + Waltz (1972): Compute labeling through local propagation. Constraints Outline Interpreting line diagrams Constraint modeling Constraint propagation Constraint satisfaction problems (CSP) aka constraint programs (CP). Solving CSPs Case study: Scheduling (Appendix) Brian Williams, Fall 10 8 4
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1. Limited line interpretations: No shadows or cracks . 2. Three-faced vertices: Intersection of exactly three object faces (e.g., no pyramid tops). 3. General position: Small perturbations of selected viewing points can not lead to a change in junction type. Brian Williams, Fall 10 9 Modeling: Systematically derive all realizable junction types Consider: a three face vertex, which divides space into octants , (not guaranteed to be at right angles) , and all possible fillings of octants, viewed from all empty octants. Brian Williams, Fall
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MIT16_410F10_lec05 - Constraint Programming: Modeling, Arc...

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