Projectice subgroups for grouping

The history of grouping in computer vision stretches a long way back. One strand could be called geometry–based and focuses on shapes with special regularities such as symmetry. From a mathematical point of view, the subparts of such shapes are related by special transformations. The presented work proposes to systematically classify such ‘special’ transformations by studying projective subgroups that come with fixed structures. These are geometric entities such as points or lines that remain fixed under the projectivities in the subgroups. As subgroups have their own invariants, these can then be used to guide the search for the corresponding groupings.

[1]  M. Wertheimer.  Laws of organization in perceptual forms. , 1938 .

[2]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[3]  C. E. Springer,et al.  Geometry and Analysis of Projective Spaces , 1967 .

[4]  Takeo Kanade,et al.  Recovery of the Three-Dimensional Shape of an Object from a Single View , 1981, Artif. Intell..

[5]  L. Gool,et al.  Semi-differential invariants , 1992 .

[6]  J. Lapresté,et al.  Locating and modelling a flat symmetric object from a single perspective image , 1993 .

[7]  David A. Forsyth,et al.  Class-based grouping in perspective images , 1995, Proceedings of IEEE International Conference on Computer Vision.

[8]  Luc Van Gool,et al.  Groups for Grouping: A Strategy for the Exploitation of Geometrical Constraints , 1995, CAIP.

[9]  Luc Van Gool,et al.  Mirror and point symmetry under perspective skewing , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[10]  Charlie Rothwell,et al.  Understanding the Shape Properties of Trihedral Polyhedra , 1996, ECCV.

[11]  Luc Van Gool,et al.  A Systematic Approach to Geometric-Based Grouping and Non-accidentalness , 1997, AFPAC.

[12]  Luc Van Gool,et al.  The Cascaded Hough Transform as Support for Grouping and Finding Vanishing Points and Lines , 1997, AFPAC.

[13]  Luc Van Gool,et al.  The cascaded Hough transform as an aid in aerial image interpretation , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[14]  David G. Lowe,et al.  Perceptual Organization and Visual Recognition , 2012 .