Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. This paper closes this gap by proposing a novel optimisation formulation for isometric multi-shape matching. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis. Our algorithm obtains multi-matchings that are by construction provably cycle-consistent. We demonstrate the superior performance of our method on various datasets and set the new state-of-the-art in isometric multi-shape matching.
NICTA（澳大利亚国家信息与通信技术研究院）；Australian National University（澳大利亚国立大学）
Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related by "almost isometric" transformations, are actually subject not only to noise but also, to some limited degree, to variations in appearance and scale. In this paper, we introduce a graphical model that parameterises appearance, distance, and angle features and we learn all of the involved parameters via structured prediction. The outcome is a model for near-r…
Università della Svizzera italiana（瑞士意大利语大学）；École Polytechnique（巴黎综合理工学院）；EDF R&D（法国电力公司研发部）
We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead 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…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Saarland University（萨尔大学）
Intrinsic isometric shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency, i.e., the metric structure of the whole manifold must not change significantly. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Partial matching is particularly important for robustness to topological noise (incomplete data and contacts), which is a common problem in real-world 3D scanner data. In this paper, we introduce a new approach to p…
Creating representations of shapes that are invari-ant to isometric or almost-isometric transforma-tions has long been an area of interest in shape anal-ysis, since enforcing invariance allows the learningof more effective and robust shape representations.Most existing invariant shape representations arehandcrafted, and previous work on learning shaperepresentations do not focus on producing invariantrepresentations. To solve the problem of learningunsupervised invariant shape representations, weuse contrastive learning, which produces discrimi-native representations through learning invarianc…
In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution hyperparameter, which can severely affect the overall accuracy or lead to overfitting, if not chosen carefully. In this paper, we show that spectral resolution tuning can be alleviated by introducing spectral attention. Our framework is applicable in both supervised and unsupervised settings, and we show that it is possible to train the network so that it can ada…
We present the first utterly self-supervised network for dense correspondence mapping between non-isometric shapes. The task of alignment in non-Euclidean domains is one of the most fundamental and crucial problems in computer vision. As 3D scanners can generate highly complex and dense models, the mission of finding dense mappings between those models is vital. The novelty of our solution is based on a cyclic mapping between metric spaces, where the distance between a pair of points should remain invariant after the full cycle. As the same learnable rules that generate the point-wise descript…
Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between all possible pairs of points on the 3D shape manifold. In the proposed representation, the normal curvature along the quasi-geodesic paths between any two points on the shape surface is preserved. We employ the eigenspectrum of the proposed global representation to address the problems of determination of region-based correspondence between isometric shapes…
Indian Institute of Technology, Jodhpur（焦特布尔印度理工学院）；MPI for Informatics（马克斯·普朗克信息学研究所）；Universität Siegen（锡根大学）
Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, $\mathcal{NP}$-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 multi-matching; in addition, it is also cycle-consistent. Its iterative formulation is admissible…
University of Science and Technology of China（中国科学技术大学）
Depth scans acquired from different views may contain nuisances such as noise, occlusion, and varying point density. We propose a novel Signature of Geometric Centroids descriptor, supporting direct shape matching on the scans, without requiring any preprocessing such as scan denoising or converting into a mesh. First, we construct the descriptor by voxelizing the local shape within a uniquely defined local reference frame and concatenating geometric centroid and point density features extracted from each voxel. Second, we compare two descriptors by employing only corresponding voxels that are…
Unsupervised Contrastive Learning for Efficient and Robust Spectral Shape Matching
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；Research Center for Data Hub and Security, Zhejiang Lab（浙江实验室数据枢纽与安全研究中心）
We present G-MSM (Graph-based Multi-Shape Matching), a novel unsupervised learning approach for non-rigid shape correspondence. Rather than treating a collection of input poses as an unordered set of samples, we explicitly model the underlying shape data manifold. To this end, we propose an adaptive multi-shape matching architecture that constructs an affinity graph on a given set of training shapes in a self-supervised manner. The key idea is to combine putative, pairwise correspondences by propagating maps along shortest paths in the underlying shape graph. During training, we enforce cycle-…
TU Munich（慕尼黑工业大学）；Technion（以色列理工学院）；TAU（特拉维夫大学）；Sapienza University of Rome（罗马大学）；USI Lugano（卢加诺大学）；Intel（英特尔）
We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We prov…
Imperial College（帝国理工学院）；University of Copenhagen（哥本哈根大学）
Matching of images and analysis of shape differences is traditionally pursued by energy minimization of paths of deformations acting to match the shape objects. In the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, iterative gradient descents on the matching functional lead to matching algorithms informally known as Beg algorithms. When stochasticity is introduced to model stochastic variability of shapes and to provide more realistic models of observed shape data, the corresponding matching problem can be solved with a stochastic Beg algorithm, similar to the finite tempera…
The current state-of-the-art hand gesture recognition methodologies heavily rely in the use of machine learning. However there are scenarios that machine learning cannot be applied successfully, for example in situations where data is scarce. This is the case when one-to-one matching is required between a query and a dataset of hand gestures where each gesture represents a unique class. In situations where learning algorithms cannot be trained, classic computer vision techniques such as feature extraction can be used to identify similarities between objects. Shape is one of the most important …
Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings in virtue of their invariance to change of pose. Classical graph isomorphism schemes relying on the ordering of the eigenvalues to align the eigenspaces fail when handling large data-sets or noisy data. We derive a new formulation that finds the best alignment between two congruent $K$-dimensional sets of points by selecting …
LIX（巴黎综合理工学院计算机实验室）；Ecole Polytechnique, IP Paris（巴黎综合理工学院（巴黎理工学院））
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the different shapes in high-dimensional space where the matching is easier to solve is a well-trodden path that has given many outstanding solutions. Recently, a new trend has shown advantages in learning such representations. This novel idea motivated us to investigate which properties differentiate these data-driven embeddings and which ones promote state-of-the-…
TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisation
Italian Institute of Technology（意大利理工学院）；University of Genoa（热那亚大学）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；University of Bonn（波恩大学）；Lamarr Institute（拉马尔研究所）；University of Verona（维罗纳大学）
GLASS: Graph and Vision-Language Assisted Semantic Shape Correspondence
Hong Kong Polytechnic University, HK SAR（香港理工大学）；Fondazione Bruno Kessler, Italy（布鲁诺·凯斯勒基金会）；Laboratory for Artificial Intelligence in Design, HK SAR（设计中的人工智能实验室）；University of Technology Sydney, Australia（悉尼科技大学）
Universität Siegen（锡根大学）；Sapienza Università di Roma（罗马大学）；Università della Svizzera Italiana（提契诺大学）；Technische Universität München（慕尼黑工业大学）
We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem as finding the shortest circular path on the product 3-manifold of the surface and the curve. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of $O(mn^2\log(n))$, where $m$ and $n$ denote the number of vertices on the template curve and the 3D shape respectively. We also demonstrate that in practice the ru…
Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class variations, local deformations, articulations, viewpoint changes and missed and extraneous contour portions due to errors in shape extraction. While small local deformations has been handled in the literature by allowing some leeway in the matching of individual contour points via methods such as Chamfer distance and Hausdorff distance, handling more severe deformat…
LIGM (UMR 8049) École des Ponts UPE（巴黎桥路大学LIGM实验室（法国国家科研中心8049混合研究单位））；Adobe Research（奥多比研究院）
We propose a self-supervised approach to deep surface deformation. Given a pair of shapes, our algorithm directly predicts a parametric transformation from one shape to the other respecting correspondences. Our insight is to use cycle-consistency to define a notion of good correspondences in groups of objects and use it as a supervisory signal to train our network. Our method does not rely on a template, assume near isometric deformations or rely on point-correspondence supervision. We demonstrate the efficacy of our approach by using it to transfer segmentation across shapes. We show, on Shap…
Netaji Subhas Institute of Technology（内塔吉·苏巴斯理工学院）；The University of Georgia（佐治亚大学）
An end-to-end trainable ConvNet architecture, that learns to harness the power of shape representation for matching disparate image pairs, is proposed. Disparate image pairs are deemed those that exhibit strong affine variations in scale, viewpoint and projection parameters accompanied by the presence of partial or complete occlusion of objects and extreme variations in ambient illumination. Under these challenging conditions, neither local nor global feature-based image matching methods, when used in isolation, have been observed to be effective. The proposed correspondence determination sche…
Finding a template in a search image is an important task underlying many computer vision applications. Recent approaches perform template matching in a deep feature-space, produced by a convolutional neural network (CNN), which is found to provide more tolerance to changes in appearance. In this article we investigate if enhancing the CNN's encoding of shape information can produce more distinguishable features that improve the performance of template matching. This investigation results in a new template matching method that produces state-of-the-art results on a standard benchmark. To confi…
In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We a…
We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps. Secondly, the network is trained with edge maps of landmark images, which are automatically obtained by a structure-from-motion pipeline. The learned representation is evaluated on a range of different tasks, providing improvements on challenging cases of domain generalization, generic sketch-based image retrieval or its fine-grained counterpart. In contrast to oth…
Osaka University（大阪大学）；Japan Science and Technology Agency（日本科学技术振兴机构）
This paper proposes a multi-view extension of instance segmentation without relying on texture or shape descriptor matching. Multi-view instance segmentation becomes challenging for scenes with repetitive textures and shapes, e.g., plant leaves, due to the difficulty of multi-view matching using texture or shape descriptors. To this end, we propose a multi-view region matching method based on epipolar geometry, which does not rely on any feature descriptors. We further show that the epipolar region matching can be easily integrated into instance segmentation and effective for instance-wise 3D …
Establishing a correspondence between two non-rigidly deforming shapes is one of the most fundamental problems in visual computing. Existing methods often show weak resilience when presented with challenges innate to real-world data such as noise, outliers, self-occlusion etc. On the other hand, auto-decoders have demonstrated strong expressive power in learning geometrically meaningful latent embeddings. However, their use in \emph{shape analysis} has been limited. In this paper, we introduce an approach based on an auto-decoder framework, that learns a continuous shape-wise deformation field…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of object-typical statistical variations is achieved by introducing degrees of freedom that describe transformations and deformations of the shape template. The shape model is mathematically equivalent to contour-based approaches but inference can be performed without conversion between the contour and region representations, allowing combination with other convex segmenta…
University of Zagreb, Faculty of Electrical Engineering and Computing（萨格勒布大学电气工程与计算学院）；Linköping University（林雪平大学）
Current best local descriptors are learned on a large dataset of matching and non-matching keypoint pairs. However, data of this kind is not always available since detailed keypoint correspondences can be hard to establish. On the other hand, we can often obtain labels for pairs of keypoint bags. For example, keypoint bags extracted from two images of the same object under different views form a matching pair, and keypoint bags extracted from images of different objects form a non-matching pair. On average, matching pairs should contain more corresponding keypoints than non-matching pairs. We …
We propose a novel technique, termed compact shape trees, for computing correspondences of single-boundary 2-D shapes in O(n2) time. Together with zero or more features defined at each of n sample points on the shape's boundary, the compact shape tree of a shape comprises the O(n) collection of vectors emanating from any of the sample points on the shape's boundary to the rest of the sample points on the boundary. As it turns out, compact shape trees have a number of elegant properties both in the spatial and frequency domains. In particular, via a simple vector-algebraic argument, we show tha…
Institute of Computer Science and Technology, Peking University（北京大学计算机科学技术研究所）；Texas A&M University（德克萨斯农工大学）；Adobe Research（奥多比研究中心）
Artistic text style transfer is the task of migrating the style from a source image to the target text to create artistic typography. Recent style transfer methods have considered texture control to enhance usability. However, controlling the stylistic degree in terms of shape deformation remains an important open challenge. In this paper, we present the first text style transfer network that allows for real-time control of the crucial stylistic degree of the glyph through an adjustable parameter. Our key contribution is a novel bidirectional shape matching framework to establish an effective …
We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline, and propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings. Specifically, we first formulate the Dirichlet energy of the pulled-back shape coordinates, as a way to evaluate smoothness of a pointwise map across discrete surfaces. We then extend the recently proposed discrete solver and show how a strategy based on auxiliary variable reformulation allows us to optimize pointwise map smoothness alongside desirable functional map properties such …
