Criteriashape

Criteriashape is a concept in computational geometry and data analysis that quantifies how closely a geometric shape meets a predefined set of criteria. It serves as both a descriptor and a scoring function used in shape matching, segmentation, and model selection. A criteriashape score can be a scalar or a vector, with components corresponding to attributes such as smoothness, convexity, symmetry, compactness, or adherence to a target contour.

Calculation typically involves assigning normalized scores to individual criteria and combining them through a weighted sum, a multiobjective optimization, or a probabilistic model. Normalization is important to make scores comparable across scales. In practice, common criteria include area-to-perimeter ratio, curvature distribution, Euler characteristic, Hausdorff distance to a reference shape, and symmetry measures. Depending on the application, some criteria may be differentiable to allow gradient-based optimization, while others are used in discrete selection.

Applications include shape-based model fitting, image segmentation refinement, shape priors in probabilistic inference, and quality control in manufacturing or geographic information systems where shapes must satisfy regulatory or design constraints. Methodologically, criteriashape sits at the intersection of shape descriptors, regularization terms, and multi-criteria decision-making. It differs from simple shape descriptors by embedding explicit constraint satisfaction into a single score or objective. Limitations include dependency on chosen criteria and weights, sensitivity to noise, and potential loss of interpretability when multiple criteria conflict.

See also: shape prior, regularization, shape descriptor, multi-criteria optimization, shape matching.