Well-composed images and rigid transformations

We study the conditions under which the topological properties of a 2D well-composed binary image are preserved under arbitrary rigid transformations. This work initiates a more global study of digital image topological properties under such transformations, which is a crucial but under-considered problem in the context of image processing, e.g., for image registration and warping.

[1]  Nicolas Passat,et al.  Topology Preserving Warping of 3-D Binary Images According to Continuous One-to-One Mappings , 2011, IEEE Transactions on Image Processing.

[2]  Christopher Conrad,et al.  Preserving Topology by a Digitization Process , 1998, Journal of Mathematical Imaging and Vision.

[3]  Azriel Rosenfeld,et al.  Adjacency in Digital Pictures , 1974, Inf. Control..

[4]  Didier Arquès,et al.  Thinning grayscale well-composed images , 2004, Pattern Recognit. Lett..

[5]  Christopher Conrad,et al.  Conditions that Guarantee a Digitization Process Preserves Topology , 1995, DAGM-Symposium.

[6]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[7]  Pierre Soille,et al.  Advances in mathematical morphology applied to geoscience and remote sensing , 2002, IEEE Trans. Geosci. Remote. Sens..

[8]  Jean Paul Frédéric Serra.  Connectivity on Complete Lattices , 2004, Journal of Mathematical Imaging and Vision.

[9]  Fabrice Heitz,et al.  3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization , 2005, IEEE Transactions on Image Processing.

[10]  Longin Jan Latecki,et al.  Digital Topology , 1994 .

[11]  Azriel Rosenfeld,et al.  Topology-Preserving Deformations of Two-Valued Digital Pictures , 1998, Graph. Model. Image Process..

[12]  Longin Jan Latecki,et al.  Digitizations Preserving Topological and Differential Geometric Properties , 1995, Comput. Vis. Image Underst..

[13]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology. I Dilations and erosions , 1990, Comput. Vis. Graph. Image Process..

[14]  Daniel Rueckert,et al.  Information Processing in Medical Imaging (IPMI) , 2013 .

[15]  Pierre-Louis Bazin,et al.  Digital Homeomorphisms in Deformable Registration , 2007, IPMI.

[16]  Jerry L. Prince,et al.  Digital Topology in Brain Imaging , 2010, IEEE Signal Processing Magazine.

[17]  Azriel Rosenfeld,et al.  Well-Composed Sets , 1995, Comput. Vis. Image Underst..

[18]  Eric Rémila,et al.  Configurations induced by discrete rotations: periodicity and quasi-periodicity properties , 2005, Discret. Appl. Math..

[19]  Vladimir A. Kovalevsky,et al.  Finite topology as applied to image analysis , 1989, Comput. Vis. Graph. Image Process..

[20]  Michel Couprie,et al.  Digital Imaging: A Unified Topological Framework , 2011, Journal of Mathematical Imaging and Vision.

[21]  Efim Khalimsky,et al.  Topological structures in computer science , 1987 .

[22]  Hugues Talbot,et al.  Combinatorial structure of rigid transformations in 2D digital images , 2013, Comput. Vis. Image Underst..

[23]  Jacques-Olivier Lachaud,et al.  Fully deformable 3D digital partition model with topological control , 2011, Pattern Recognit. Lett..

[24]  Longin Jan Latecki.  3D Well-Composed Pictures , 1997, CVGIP Graph. Model. Image Process..

[25]  Christian Ronse,et al.  Set-Theoretical Algebraic Approaches to Connectivity in Continuous or Digital Spaces , 2004, Journal of Mathematical Imaging and Vision.

[26]  Hugues Talbot,et al.  Sufficient Conditions for Topological Invariance of 2D Images under Rigid Transformations , 2013, DGCI.

[27]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology : II. Openings and closings , 1991, CVGIP Image Underst..

[28]  Longin Jan Latecki.  Multicolor well-composed pictures , 1995, Pattern Recognit. Lett..