The Euclidean distance transform
Abstract
The medial-axis transform (MAT), also called skeleton, is a shape abstraction proposed by computer vision, and has a number of important engineering applications such as finite-element mesh generation. The theory for the MAT of 2D solids is investigated. We prove the uniqueness, divisibility and connectedness properties of the MAT of 2D solids. Algorithms are proposed to extract the MAT based on two criteria, the maximal circle criterion and the equal distance criterion. The algorithms which use the maximal circle criterion produce the MAT along with many noisy point, and further refinement using a threshold value is needed. The algorithms which use the equal distance criterion walk along the MAT from a starting MAT point. Because the connectedness property, we can find all of the MAT if a good strategy is used to walk along the MAT. Systems of equations are generated so that Newton iteration can be applied, and new MAT points can be found. The algorithms can be extended to 3D with more complex data structure. Detecting self-intersections in offsets is a problem that has both a mathematical and a combinatorial character. Some self-intersections can be detected based on local criteria applied to boundary elements, but others require evaluating the spatial relationship between unknown parts of the base curve, and this is difficult for the traditional offset algorithms. We solve the problem by applying the Euclidean distance transform having suitably discretized the geometric shapes. Several strategies are presented and are compared for efficiency and performance.
Degree
Ph.D.
Advisors
Hoffmann, Purdue University.
Subject Area
Computer science
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.