Linear Shape Deformation Models with Local Support Using Graph-Based Structured Matrix Factorisation

Abstract

α = +[ PCA (global support) Our (local support) PCA (global support) Our (local support) PCA (global support)Our (local support)Global support factors of PCA lead to implausible body shapes, whereas the local support factors of our method give more realistic results. See our accompanying video for animated results. AbstractRepresenting 3D shape deformations by highdimensional linear models has many applications in computer vision and medical imaging. Commonly, using Principal Components Analysis a low-dimensional subspace of the high-dimensional shape space is determined. However, the resulting factors (the most dominant eigenvectors of the covariance matrix) have global support, i.e. changing the coefficient of a single factor deforms the entire shape. Based on matrix factorisation with sparsity and graph-based regularisation terms, we present a method to obtain deformation factors with local support. The benefits include better flexibility and interpretability as well as the possibility of interactively deforming shapes locally. We demonstrate that for brain shapes our method outperforms the state of the art in local support models with respect to generalisation and sparse reconstruction, whereas for body shapes our method gives more realistic deformations. 0 c 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Multi‐mother wavelet neural network‐based on genetic algorithm and multiresolution analysis for fast 3D mesh deformation

“…Although for the horse dataset, the method [24] has an error equal to 29.6090 and 20.1994 in [21], 18.0624 in [23], 12.9605 in [25], and 7.3682 in [20], compared to 6.4412 in our work. It is clear that the obtained error rate is so reduced and the performance of a MA on the synthesised mesh allows to minimise the resolution without losing the initial data, reaching the control mesh.…”

“…Indeed, our deformation algorithm gives a good reconstructed object and is more performing as it has better quantitative reconstruction findings than the existing technique having lower reconstruction errors when enough components are employed. Visual results shown in [20, 21, 23, 25] did not deal intensively with large‐scale rotations and could not reform possible models in such cases. Nevertheless, Wang et al .…”

“…We use the generalisation ability error (root mean square) to ensure the comparison on the set of tests of our method with several state‐of‐the‐art methods, including original sparse localised deformation component (SPLOCS) [20], SPLOCS with deformation gradients [23], SPLOCS with edge lengths and dihedral angles [24], SPLOCS with the feature from [21], and mesh‐based autoencoders for localised deformation component analysis [25].…”

“…The deformation components from the PCA are broadly supported, which are not intuitive for mesh editing and deformation, especially when the user needs to deform the mesh locally in the spatial domain [19]. By including spatial constraints, a sparsity term is used to extract localised deformation components [20, 21], which achieve better than region‐based PCA variants (clustered PCA) [22], in terms of extracting meaningful localised deformation components. Though, it employs Euclidean coordinates which cannot represent meshes with large rotations.…”

Sparse Data Driven Mesh Deformation

“…Deformation representation is important for effective data-driven deformation. Euclidean coordinates are the most straightforward way [36], [43], although with obvious limitations for rotations. More effective deformation gradients are used to represent shape deformations [5], [37], which still cannot handle large rotations.…”