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Rigid shapes should be naturally compared up to rigid motion or isometry,which preserves all inter-point distances. The same rigid shape can be oftenrepresented by noisy point clouds of different sizes. Hence the isometry shaperecognition problem requires methods that are independent of a cloud size. Thispaper studies stable-under-noise isometry invariants for the recognitionproblem stated in the harder form when given clouds can be related by affine orprojective transformations. The first contribution is the stability proof forthe invariant mergegram, which completely determines a single-linkagedendrogram in general position. The second contribution is the experimentaldemonstration that the mergegram outperforms other invariants in recognizingisometry classes of point clouds extracted from perturbed shapes in images.

Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence