Shape registration with directional data

Abstract

We propose several cost functions for registration of shapes encoded with Euclidean and/or non-Euclidean information (unit vectors). Our framework is assessed for estimation of both rigid and non-rigid transformations between the target and model shapes corresponding to 2D contours and 3D surfaces. The experimental results obtained confirm that using the combination of a point's position and unit normal vector in a cost function can enhance the registration results compared to state of the art methods.

Comparing Seven Methodogies for Rigid Alignment of Point Clouds with Focus on Frame-to-Frame Registration in Depth Sequences

“…As further works, we should observe that the CTSF can be used as a dissimilarity factor between any second order tensors and applied in tasks other than rigid registration. Therefore, a new avenue is to apply this criterion in non-rigid alignments problems and compare its performance with counterpart ones [9], [48], [49] in a more general registration scenario.…”

“…The scale of the mean rotation/translation errors in Figure 22 do not allow to rank the best techniques. To solve this problem, we report in Tables IX-X the best seven methods according to the rotation and translation errors with the corresponding standard deviations calculated by expression (49) and (50), respectively.…”

“…From Table IX, it is noticeable that Sparse ICP-CTSF and Sparse ICP are the best techniques for rotation, with a small advantage of former with k = 50% against the latter. We shall TABLE IX: Best seven methods for video 'freiburg2 rpy' according to the rotation average (equation (47)) with standard deviations given by expression (49).…”

“…Best seven methods for video 'freiburg2 xyz' according to the rotation average (equation(47)) with standard deviations given by expressions(49).…”

Characterising shape patterns using features derived from best-fitting ellipsoids

“…Additional recent work on shape analysis includes a "bag of words" approach [22], a moment invariant approach for disconnected shapes [23], shape registration in the context of directional data [24], scalable methods [25], extensions of landmark methods [26], extensions of chamfer matching [27], characterising 50 shape by modelling electric charge distributions (similar to ideas used for skeletonisation), extension of shape context [28], methods based on depicting the overall shape as a union of ellipses [29] and unsupervised learning methods [30].…”