scholarly journals Automated transformation-invariant shape recognition through wavelet multiresolution

2001 ◽  
Author(s):  
Patrice Brault ◽  
Hugues Mounier
Keyword(s):  
Shape Recognition ◽  
Invariant Shape

Affine-invariant Shape Recognition Using Grassmann Manifold

2012 ◽  
Vol 38 (2) ◽  
pp. 248-258 ◽  
Author(s):  
Yun-Peng LIU ◽  
Guang-Wei LI ◽  
Ze-Lin SHI
Keyword(s):  
Grassmann Manifold ◽  
Shape Recognition ◽  
Affine Invariant ◽  
Invariant Shape

scholarly journals Isometry Invariant Shape Recognition of Projectively Perturbed Point Clouds by the Mergegram Extending 0D Persistence

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2121
Author(s):  
Yury Elkin ◽  
Vitaliy Kurlin
Keyword(s):  
General Position ◽  
Shape Recognition ◽  
Rigid Motion ◽  
Point Clouds ◽  
Recognition Problem ◽  
Experimental Demonstration ◽  
Single Linkage ◽  
Projective Transformations ◽  
The Stability ◽  
Invariant Shape

Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point clouds of different sizes. Hence, the isometry shape recognition problem requires methods that are independent of a cloud size. This paper studies stable-under-noise isometry invariants for the recognition problem stated in the harder form when given clouds can be related by affine or projective transformations. The first contribution is the stability proof for the invariant mergegram, which completely determines a single-linkage dendrogram in general position. The second contribution is the experimental demonstration that the mergegram outperforms other invariants in recognizing isometry classes of point clouds extracted from perturbed shapes in images.

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