Boundary Detection by Constrained Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
On active contour models and balloons
CVGIP: Image Understanding
Set-Valued Means of Random Particles
Journal of Mathematical Imaging and Vision
Averaging of Random Sets Based on Their Distance Functions
Journal of Mathematical Imaging and Vision
Deformable template models: a review
Signal Processing - Special issue on deformable models and techniques for image and signal processing
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Efficient deformable template detection and localization without user initialization
Computer Vision and Image Understanding
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Boundary reconstruction in binary images using splines
Pattern Recognition
Bootstrap confidence sets for the Aumann mean of a random closed set
Computational Statistics & Data Analysis
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Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing definitions of the expected set rely on different criteria to construct the expectation. This paper introduces new definitions of the expected set and the expected boundary, based on oriented distance functions. The proposed expectations have a number of attractive properties, including inclusion relations, convexity preservation and equivariance with respect to rigid motions. The paper introduces a special class of decomposable oriented distance functions for parametric sets and gives the definition and properties of decomposable random closed sets. Further, the definitions of the empirical mean set and the empirical mean boundary are proposed and empirical evidence of the consistency of the boundary estimator is presented. In addition, the paper discusses loss functions for set inference in frequentist framework and shows how some of the existing expectations arise naturally as optimal estimators. The proposed definitions are illustrated on theoretical examples and real data.