Luca Cosmo

Partial Functional Correspondence

In this paper, we propose a method for computing partial functional correspondence between non‐rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford–Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.

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.

Consistent Partial Matching of Shape Collections via Sparse Modeling

Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle‐consistency—namely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle‐consistent maps; in order to allow for partially similar and extra‐class shapes, we formulate the problem as a series of quadratic programs with sparsity‐inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes.

Matching Deformable Objects in Clutter

We consider the problem of deformable object detection and dense correspondence in cluttered 3D scenes. Key ingredient to our method is the choice of representation: we formulate the problem in the spectral domain using the functional maps framework, where we seek for the most regular nearly-isometric parts in the model and the scene that minimize correspondence error. The problem is initialized by solving a sparse relaxation of a quadratic assignment problem on features obtained via data-driven metric learning. The resulting matching pipeline is solved efficiently, and yields accurate results in challenging settings that were previously left unexplored in the literature.

A Robust Multi-camera 3D Ellipse Fitting for Contactless Measurements

Ellipses are a widely used cue in many 2D and 3D object recognition pipelines. In fact, they exhibit a number of useful properties. First, they are naturally occurring in many man-made objects. Second, the projective invariance of the class of ellipses makes them detectable even without any knowledge of the acquisition parameters. Finally, they can be represented by a compact set of parameters that can be easily adopted within optimization tasks. While a large body of work exists in the literature about the localization of ellipses as 2D entities in images, less effort has been put in the direct localization of ellipses in 3D, exploiting images coming from a known camera network. In this paper we propose a novel technique for fitting elliptical shapes in 3D space, by performing an initial 2D guess on each image followed by a multi-camera optimization refining a 3D ellipse simultaneously on all the calibrated views. The proposed method is validated both with synthetic data and by measuring real objects captured by a specially crafted imaging head. Finally, to evaluate the feasibility of the approach within real-time industrial scenarios, we tested the performance of a GPU-based implementation of the algorithm.

Camera Calibration from Coplanar Circles

The estimation of camera intrinsic parameters plays a crucial role in all computer vision tasks for which the underlying model that drives the image formation process has to be known. As a consequence, a deluge set of different approaches has been proposed in literature over the last decades. Most of those lean on the observation of a known object (i.e. a calibration target) from different point of views, providing the necessary data to estimate the model through different optimization approaches. In this work, we exploit the projective properties of conics to estimate the focal length and optical center of a pinhole camera just by observing a set of coplanar circles, where neither the radius nor the reciprocal position of each circle has to be known a-priori. This make such method particularly interesting whenever the usage of a calibration target is not a feasible option. Our contribution is twofold. First, we propose a reliable method to locate coplanar circles from images by means of a non-cooperative evolutionary game. Second, we refine the estimation of camera parameters with a non-linear function minimization through a simple yet effective gradient descent. Performance of the proposed approach is assessed through an experimental section consisting on both quantitative and qualitative tests.

Adopting an unconstrained ray model in light-field cameras for 3D shape reconstruction

Given the raising interest in light-field technology and the increasing availability of professional devices, a feasible and accurate calibration method is paramount to unleash practical applications. In this paper we propose to embrace a fully non-parametric model for the imaging and we show that it can be properly calibrated with little effort using a dense active target. This process produces a dense set of independent rays that cannot be directly used to produce a conventional image. However, they are an ideal tool for 3D reconstruction tasks, since they are highly redundant, very accurate and they cover a wide range of different baselines. The feasibility and convenience of the process and the accuracy of the obtained calibration are comprehensively evaluated through several experiments.

Partial matching of deformable shapes

Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods.

Design and Evaluation of a Viewer-Dependent Stereoscopic Display

Traditional stereoscopic displays assume the viewer to be standing at a specific location, that is the same pose (relative to the screen) of the stereo camera pair that depicted the scene (physically or virtually). Even for basic applications, such as movies or games, this leads to visual inconsistencies as soon as the user moves his head. Moreover, with this premises, it is not possible at all to develop more sophisticated 3D applications, involving the freedom for the user to walk around objects or to interact with them. The most popular solution to these limitation is to track the user head in order to produce a scene rendering that can be seen correctly from his point of view. With this paper we propose a viewer-dependent system that is very easy to implement since it is based on a simple augmentation of basic shutter glasses used in standard stereoscopic setups. Furthermore, we introduce a practical and sound method to quantitatively assess the accuracy of any view-dependent display approach. This fills a clear shortcoming of the currently adopted evaluation methods, that are for the most part qualitative.

Using multiple sensors for reliable markerless identification through supervised learning

In many interaction models involving an active surface, there is a need to identify the specific object that performs an action. This is the case, for instance, when interactive contents are selected through differently shaped physical objects, or when a two-way communication is sought as the result of a touch event. When the technological facility is based on image processing, fiducial markers become the weapon of choice in order to associate a tracked object to its identity. Such approach, however, requires a clear and unoccluded view of the marker itself, which is not always the case. We came across this kind of hurdle during the design of a very large multi-touch interactive table. In fact, the thickness of the glass and the printed surface, which were required for our system, produced both blurring and occlusion at a level such that markers were completely unreadable. To overcome these limitations we propose an identification approach based on SVM that exploits the correlation between the optical features of the blob, as seen by the camera, and the data coming from active sensors available on the physical object that interacts with the table. This way, the recognition has been cast into a classification problem that can be solved through a standard machine learning framework. The resulting approach seems to be general enough to be applied in most of the problems where disambiguation can be achieved through the comparison of partial data coming from multiple simultaneous sensor readings. Finally, an extensive experimental section assesses the reliability of the identification.