Sampling Relevant Points for Surface Registration

Surface registration is a fundamental step in the reconstruction of three-dimensional objects. This is typically a two-step process where an initial coarse motion estimation is followed by a refinement step that almost invariably is some variant of Iterative Closest Point (ICP), which iteratively minimizes a distance function measured between pairs of selected neighboring points. The selection of relevant points on one surface to match against points on the other surface is an important issue in any efficient implementation of ICP, with strong implications both on the convergence speed and on the quality of the final alignment. This is due to the fact that typically on a surface there are a lot of low-curvature points that scarcely constrain the rigid transformation and an order of magnitude less descriptive points that are more relevant for finding the correct alignment. This results in a tendency of surfaces to "overfit" noise on low-curvature areas sliding away from the correct alignment. In this paper we propose a novel relevant-point sampling approach for ICP based on the idea that points in an area of great change constrain the transformation more and thus should be sampled with higher frequency. Experimental evaluations confront the alignment accuracy obtained with the proposed approach with those obtained with the commonly adopted uniform subsampling and normal-space sampling strategies. © 2011 IEEE

A Non-Cooperative Game for 3D Object Recognition in Cluttered Scenes

During the last few years a wide range of algorithms and devices have been made available to easily acquire range images. To this extent, the increasing abundance of depth data boosts the need for reliable and unsupervised analysis techniques, spanning from part registration to automated segmentation. In this context, we focus on the recognition of known objects in cluttered and incomplete 3D scans. Fitting a model to a scene is a very important task in many scenarios such as industrial inspection, scene understanding and even gaming. For this reason, this problem has been extensively tackled in literature. Nevertheless, while many descriptor-based approaches have been proposed, a number of hurdles still hinder the use of global techniques. In this paper we try to offer a different perspective on the topic. Specifically, we adopt an evolutionary selection algorithm in order to extend the scope of local descriptors to satisfy global pairwise constraints. In addition, the very same technique is also used to shift from an initial sparse correspondence to a dense matching. This leads to a novel pipeline for 3D object recognition, which is validated with an extensive set of experiments and comparisons with recent well-known feature-based approaches. © 2011 IEEE

Certification of Gaussian Boson Sampling via graphs feature vectors and kernels

Gaussian Boson Sampling (GBS) is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling (BS) problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a specific computational model. Indeed, thanks to the implementation in photonics-based processors, the latest GBS experiments have reached a level of complexity where the quantum apparatus has solved the task faster than currently up-to-date classical strategies. In addition, recent studies have identified possible applications beyond the inherent sampling task. In particular, a direct connection between photon counting of a genuine GBS device and the number of perfect matchings in a graph has been established. In this work, we propose to exploit such a connection to benchmark GBS experiments. We interpret the properties of the feature vectors of the graph encoded in the device as a signature of correct sampling from the true input state. Within this framework, two approaches are presented. The first method exploits the distributions of graph feature vectors and classification via neural networks. The second approach investigates the distributions of graph kernels. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers

An Accurate and Robust Artificial Marker Based on Cyclic Codes

Artificial markers are successfully adopted to solve several vision tasks, ranging from tracking to calibration. While most designs share the same working principles, many specialized approaches exist to address specific application domains. Some are specially crafted to boost pose recovery accuracy. Others are made robust to occlusion or easy to detect with minimal computational resources. The sheer amount of approaches available in recent literature is indeed a statement to the fact that no silver bullet exists. Furthermore, this is also a hint to the level of scholarly interest that still characterizes this research topic. With this paper we try to add a novel option to the offer, by introducing a general purpose fiducial marker which exhibits many useful properties while being easy to implement and fast to detect. The key ideas underlying our approach are three. The first one is to exploit the projective invariance of conics to jointly find the marker and set a reading frame for it. Moreover, the tag identity is assessed by a redundant cyclic coded sequence implemented using the same circular features used for detection. Finally, the specific design and feature organization of the marker are well suited for several practical tasks, ranging from camera calibration to information payload delivery

Elastic Net Constraints for Shape Matching

We consider a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes. In order to control the accuracy/sparsity trade-off we introduce a weighting parameter on the combination of two existing relaxations, namely spectral and game-theoretic. This leads to the introduction of the elastic net penalty function into shape matching problems. In combination with an efficient algorithm to project onto the elastic net ball, we obtain an approach for deformable shape matching with controllable sparsity. Experiments on a standard benchmark confirm the effectiveness of the approach. © 2013 IEEE

Structured Prediction of Dense Maps between Geometric Domains

We introduce a new framework for learning dense correspondence between deformable geometric domains such as polygonal meshes and point clouds. Existing learning based approaches model correspondence as a labelling problem, where each point of a query domain receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input geometries. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging shape correspondence benchmarks

Realistic photometric stereo using partial differential irradiance equation ratios

Shape from shading with multiple light sources is an active research area and a diverse range of approaches have been proposed in the last decades. However, devising a robust reconstruction technique still remains a challenging goal due to several highly non-linear physical factors being involved in the image acquisition process. Recent attempts at tackling the problem via photometric stereo rely on simplified hypotheses in order to make the problem solvable. Light propagation is still commonly assumed to be uniformly oriented, and the BRDF assumed to be diffuse, with limited interest for materials giving specular reflection. Taking into account realistic point light sources, in this paper we introduce a well-posed formulation based on partial differential equations for both diffuse and specular shading models. We base our derivation on the popular approach of image ratios, which makes the model independent from photometric invariants. The practical effectiveness of our method is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art

Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching

International audienceIn this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a generalpurpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through stateof-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/ DeformationBasis

Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching

International audienceIn this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a generalpurpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through stateof-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/ DeformationBasis

Learning disentangled representations via product manifold projection

We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art