Representative Shape Computation for Polygon Sets
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Solution Overview
Problem
Existing techniques for characterizing the shape of regions defined by polygons fail to accurately represent the underlying geometry, especially when dealing with concave shapes, leading to increased computational costs and inefficient visual representation.
Innovation Solution
A method is developed to compute a representative shape for a set of polygons by generating a connected graph, determining a shortest path that traverses each shape exactly once, and creating pairwise convex hulls to generate a compound hull that accurately represents the overall geometry, which can be used for various operations such as labeling, highlighting, or image classification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a minimal-area convex hull is computed for a set of points, then the computation is efficient, but the result does not meaningfully represent the visual shape of the set of points
Solution Approach 1:
The patent segments the set of points into multiple clusters using a clustering algorithm, then computes a convex hull for each cluster separately. This segmentation allows the overall hull to better represent the visual shape by capturing local structures while maintaining computational efficiency through divide-and-conquer.
Solution Approach 2:
The patent introduces an additional hierarchical dimension by organizing clusters at different levels. First, points are clustered into groups; then convex hulls are computed for each group; finally, these group hulls are combined to form the overall representative shape. This multi-level hierarchical structure enables better shape representation without proportionally increasing computational cost.
2Measurement precision
If a concave hull construction is performed to accurately represent the visual shape, then the shape representation improves, but the computational cost increases due to careful analysis requirements
Solution Approach 1:
The patent divides the complex concave hull problem into simpler convex hull subproblems by clustering points into groups. Each cluster's convex hull can be computed independently using well-established efficient algorithms, avoiding the need for complex concave hull algorithms while still achieving accurate shape representation through the hierarchical combination of these simpler hulls.
Solution Approach 2:
The patent uses multiple temporary convex hulls for different clusters as intermediate computational objects. These individual cluster hulls are computed, combined to form the overall shape representation, and then discarded. This approach replaces the need for a single complex concave hull computation with multiple simpler, disposable convex hull computations.
3Measurement precision
If further tuning is applied to create a visually representative concave hull, then the visual representation improves, but the computational cost increases
Solution Approach 1:
The patent performs preliminary clustering of points into meaningful groups before computing any hulls. This preliminary organization based on spatial relationships and density automatically captures the visual structure of the data, eliminating the need for subsequent tuning adjustments. The clustering step pre-establishes the hierarchical structure that directly yields the final shape representation.
Data Source
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AI summary
A technique for efficiently processing sets of shapes is executed by one or more processors. The technique includes receiving a description of a set of shapes, the description including an indication of geometry for each of the shapes and an indication of positioning of the shapes relative to each other; generating a connected graph containing each shape in the set to define an ordered list; for each pair of shapes adjacent to each other in the connected graph, generating a respective convex hull enclosing the pair of shapes; generating a representative shape for the set of shapes, the representative shape enclosing each of the generated convex hulls; and operating on the generated representative shape to perform an operation related to the set of shapes.