C<scp>onsistent</scp> Z<scp>oom</scp>O<scp>ut</scp>: Efficient Spectral Map Synchronization

Huang, Ruqi; Ren, Jing; Wonka, Peter; Ovsjanikov, Maks

doi:10.1111/cgf.14084

Cited by 32 publications

(26 citation statements)

References 47 publications

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“…Unfortunately, the already very high problem complexity increases even further the more shapes are used. Hence, existing multi-shape matching methods limit the total number of shapes and their resolution [12,22], work in spectral space [26], or relax the permutation constraints [28]. Early multi-matching methods computed pair-wise matchings and subsequently used permutation synchronisation to establish cycle consistency [33,38,43].…”

Section: Related Workmentioning

confidence: 99%

CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes

Bhatia¹,

Tretschk²,

Lähner³

et al. 2023

Preprint

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Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, N P-hard problem. A perfect matching is necessarily cycle-consistent: Following the pairwise point correspondences along several shapes must end up at the starting vertex of the original shape. Unfortunately, existing quantum shape-matching methods do not support multiple shapes and even less cycle consistency. This paper addresses the open challenges and introduces the first quantum-hybrid approach for 3D shape multimatching; in addition, it is also cycle-consistent. Its iterative formulation is admissible to modern adiabatic quantum hardware and scales linearly with the total number of input shapes. Both these characteristics are achieved by reducing the N -shape case to a sequence of three-shape matchings, the derivation of which is our main technical contribution. Thanks to quantum annealing, high-quality solutions with low energy are retrieved for the intermediate N Phard objectives. On benchmark datasets, the proposed approach significantly outperforms extensions to multi-shape matching of a previous quantum-hybrid two-shape matching method and is on-par with classical multi-matching methods. Our source code is available at 4dqv.mpiinf.mpg.de/CCuantuMM/.

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Section: Related Workmentioning

confidence: 99%

CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes

Bhatia¹,

Tretschk²,

Lähner³

et al. 2023

Preprint

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“…These artifacts are visible in the correspondences between pairs of shapes presented in Fig 3A .1 and 3A.2. Published studies using FM in computer graphics usually minimize such artifacts with some sort of post-processing refinement step [20,39,40]. We adopt the Consistent ZoomOut refinement technique, which iteratively and interchangeably optimizes the P2P and functional maps at multiple scales given the initial functional maps C 12 and C 21 .…”

Section: Improving Correspondences With Consistent Zoomoutmentioning

confidence: 99%

“…The Consistent ZoomOut refinement procedure hinges on a Limit Shape functional map network (FMN) analysis. Limit Shape characterizes shape variation to yield our area-based and conformal latent shape space differences (LSSDs) (see Methods and Materials section for more information) [21,24,40].…”

Section: Improving Correspondences With Consistent Zoomoutmentioning

confidence: 99%

“…The approach also considers the previous Limit Shape method as an intermediate step to produce consistent point-to-point mappings in each of the iterations. The Limit Shape method's CCLB matrices [40] provide canonically consistent bases across different shape inputs, normalizing for shape-dependent inconsistencies in the LBO. Taking advantage of these techniques, we input the learned functional maps C ij from the HSN-based descriptor learning model to the Consistent ZoomOut algorithm and obtain the point-to-point mappings and the shape differences, two major components for our study.…”

Section: Limit Shape and Consistent Zoomoutmentioning

confidence: 99%

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Automated morphological phenotyping using learned shape descriptors and functional maps: A novel approach to geometric morphometrics

Thomas

Shen

et al. 2021

Preprint

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The methods of geometric morphometrics are commonly used to quantify morphology in a broad range of biological sciences. The application of these methods to large datasets is constrained by manual landmark placement limiting the number of landmarks and introducing observer bias. To move the field forward, we need to automate morphological phenotyping in ways that capture comprehensive representations of morphological variation with minimal observer bias. Here, we present Morphological Variation Quantifier (morphVQ), a shape analysis pipeline for quantifying, analyzing, and exploring shape variation in the functional domain. morphVQ uses descriptor learning to estimate the functional correspondence between whole triangular meshes in lieu of landmark configurations. With functional maps between pairs of specimens in a dataset we can analyze and explore shape variation. morphVQ uses Consistent ZoomOut refinement to improve these functional maps and produce a new representation of shape variation, area-based and conformal (angular) latent shape space differences (LSSDs). We compare this new representation of shape variation to shape variables obtained via manual digitization and auto3DGM, an existing approach to automated morphological phenotyping. We find that LSSDs compare favorably to modern 3DGM and auto3DGM while being more computationally efficient. By characterizing whole surfaces, our method incorporates more morphological detail in shape analysis. We can classify known biological groupings, such as Genus affiliation with comparable accuracy. The shape spaces produced by our method are similar to those produced by modern 3DGM and to auto3DGM, and distinctiveness functions derived from LSSDs show us how shape variation differs between groups. morphVQ can capture shape in an automated fashion while avoiding the limitations of manually digitized landmarks, and thus represents a novel and computationally efficient addition to the geometric morphometrics toolkit.

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“…Functional map methods [ OCB*17 ] constitute a highly effective shape matching framework, especially when coupled with powerful recent post‐processing tools such as ZoomOut and its variants [ MRR*19 , HRWO20 ]. The existing methods, however, suffer from two major limitations: first, they heavily rely upon the assumption of near‐isometry, and second, they typically formulate landmark correspondence via descriptor preservation objectives, combined with other regularizers in the least squares sense.…”

Section: Introductionmentioning

confidence: 99%

Non‐Isometric Shape Matching via Functional Maps on Landmark‐Adapted Bases

Panine

Kirgo

Ovsjanikov

2022

Computer Graphics Forum

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We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional map framework, but rather than promoting isometries we focus on near-conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally-invariant energy that promotes high-quality landmark-preserving maps, and show how it can be optimized via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor-free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state-of-the-art performance on non-isometric benchmarks and near state-of-the-art performance on isometric ones.

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Consistent ZoomOut: Efficient Spectral Map Synchronization

Cited by 32 publications

References 47 publications

CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes

CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes

Automated morphological phenotyping using learned shape descriptors and functional maps: A novel approach to geometric morphometrics

Non‐Isometric Shape Matching via Functional Maps on Landmark‐Adapted Bases

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