Study of a Robust Feature: The Pointwise Lipschitz Regularity

• Published in: International journal of computer vision Vol. 88; no. 3; pp. 363 - 381
• Main Authors: Damerval, C., Meignen, S.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-07-2010; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Applied sciences; Artificial Intelligence; Computational efficiency; Computational Geometry; Computer Imaging; Computer Science; Computer science; control theory; systems; Computer vision; Deformation effects; Exact sciences and technology; Image Processing and Computer Vision; Machine vision; Mathematical analysis; Pattern Recognition; Pattern Recognition and Graphics; Pattern recognition. Digital image processing. Computational geometry; Regularity; Robustness; Studies; Transformations; Vision; Multiscale contour point detector; Invariance properties; Extraction of characteristic values; Lipschitz regularity; Robustness to geometric deformations and transformations applied to the image; Geometric transformation; Computer vision; Lipschitz condition; Image processing; Invariance; Relevance; Wavelet transformation; Multiscale method; Size effect; Robustness; Edge detection; Regularity
• ISSN: 0920-5691; 1573-1405
• DOI: 10.1007/s11263-009-0310-5

The aim of this paper is to highlight the relevance in computer vision of the pointwise Lipschitz regularity
α
∈ℝ. The regularity
α
gives a measure of the local regularity of the intensity function associated to an image. Known wavelet methods provide an efficient computation of
α
at contour points of the image. From a theoretical point of view, we study the effect of geometric deformations and other specific transformations applied to the image, showing invariance properties. From a practical point of view, we assess the robustness of the regularity
α
when the image undergoes various transformations. The results we obtain show the Lipschitz regularity
α
is a suitable feature for applications in computer vision.