Inner-Cheeger Opening and Applications

• Main Author: Velasco-Forero, Santiago
• Other Authors: Centre de Morphologie Mathématique (CMM), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2015
• Subjects: [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing; Iceland
• Online Access: https://hal.archives-ouvertes.fr/hal-01250280; https://hal.archives-ouvertes.fr/hal-01250280/document; https://hal.archives-ouvertes.fr/hal-01250280/file/InnerCheegerSet.pdf; https://doi.org/10.1007/978-3-319-18720-4_7

International audience The aim of this paper is to study an optimal opening in the sense of minimize the relationship perimeter over area. We analyze theoretical properties of this opening by means of classical results from variational calculus. Firstly, we explore the optimal radius as attribute in morphological attribute filtering for grey scale images. Secondly, an application of this optimal opening that yields a decomposition into meaningful parts in the case of binary image is explored. We provide different examples of 2D, 3D images and mesh-points datasets.