A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation

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 partial, intrinsic isometric matching. Our method is based on the observation that isometries are fully determined by purely local information: a map of a single point and its tangent space fixes an isometry for both global and the partial maps. From this idea, we develop a new representation for partial isometric maps based on equivalence classes of correspondences between pairs of points and their tangent spaces. From this, we derive a local propagation algorithm that find such mappings efficiently. In contrast to previous heuristics based on RANSAC or expectation maximization, our method is based on a simple and sound theoretical model and fully deterministic. We apply our approach to register partial point clouds and compare it to the state-of-the-art methods, where we obtain significant improvements over global methods for real-world data and stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure

Report on shape analysis and matching and on semantic matching

In GRAVITATE, two disparate specialities will come together in one working platform for the archaeologist: the fields of shape analysis, and of metadata search. These fields are relatively disjoint at the moment, and the research and development challenge of GRAVITATE is precisely to merge them for our chosen tasks. As shown in chapter 7 the small amount of literature that already attempts join 3D geometry and semantics is not related to the cultural heritage domain. Therefore, after the project is done, there should be a clear ‘before-GRAVITATE’ and ‘after-GRAVITATE’ split in how these two aspects of a cultural heritage artefact are treated.This state of the art report (SOTA) is ‘before-GRAVITATE’. Shape analysis and metadata description are described separately, as currently in the literature and we end the report with common recommendations in chapter 8 on possible or plausible cross-connections that suggest themselves. These considerations will be refined for the Roadmap for Research deliverable.Within the project, a jargon is developing in which ‘geometry’ stands for the physical properties of an artefact (not only its shape, but also its colour and material) and ‘metadata’ is used as a general shorthand for the semantic description of the provenance, location, ownership, classification, use etc. of the artefact. As we proceed in the project, we will find a need to refine those broad divisions, and find intermediate classes (such as a semantic description of certain colour patterns), but for now the terminology is convenient – not least because it highlights the interesting area where both aspects meet.On the ‘geometry’ side, the GRAVITATE partners are UVA, Technion, CNR/IMATI; on the metadata side, IT Innovation, British Museum and Cyprus Institute; the latter two of course also playing the role of internal users, and representatives of the Cultural Heritage (CH) data and target user’s group. CNR/IMATI’s experience in shape analysis and similarity will be an important bridge between the two worlds for geometry and metadata. The authorship and styles of this SOTA reflect these specialisms: the first part (chapters 3 and 4) purely by the geometry partners (mostly IMATI and UVA), the second part (chapters 5 and 6) by the metadata partners, especially IT Innovation while the joint overview on 3D geometry and semantics is mainly by IT Innovation and IMATI. The common section on Perspectives was written with the contribution of all

Virtual 3D Reconstruction of Archaeological Pottery Using Coarse Registration

The 3D reconstruction of objects has not only improved visualisation of digitised objects, it has helped researchers to actively carry out archaeological pottery. Reconstructing pottery is significant in archaeology but is challenging task among practitioners. For one, excavated potteries are hardly complete to provide exhaustive and useful information, hence archaeologists attempt to reconstruct them with available tools and methods. It is also challenging to apply existing reconstruction approaches in archaeological documentation. This limitation makes it difficult to carry out studies within a reasonable time. Hence, interest has shifted to developing new ways of reconstructing archaeological artefacts with new techniques and algorithms. Therefore, this study focuses on providing interventions that will ease the challenges encountered in reconstructing archaeological pottery. It applies a data acquisition approach that uses a 3D laser scanner to acquire point cloud data that clearly show the geometric and radiometric properties of the object’s surface. The acquired data is processed to remove noise and outliers before undergoing a coarse-to-fine registration strategy which involves detecting and extracting keypoints from the point clouds and estimating descriptions with them. Additionally, correspondences are estimated between point pairs, leading to a pairwise and global registration of the acquired point clouds. The peculiarity of the approach of this thesis is in its flexibility due to the peculiar nature of the data acquired. This improves the efficiency, robustness and accuracy of the approach. The approach and findings show that the use of real 3D dataset can attain good results when used with right tools. High resolution lenses and accurate calibration help to give accurate results. While the registration accuracy attained in the study lies between 0.08 and 0.14 mean squared error for the data used, further studies will validate this result. The results obtained are nonetheless useful for further studies in 3D pottery reassembly

How to Find More Supernovae with Less Work: Object Classification Techniques for Difference Imaging

We present the results of applying new object classification techniques to difference images in the context of the Nearby Supernova Factory supernova search. Most current supernova searches subtract reference images from new images, identify objects in these difference images, and apply simple threshold cuts on parameters such as statistical significance, shape, and motion to reject objects such as cosmic rays, asteroids, and subtraction artifacts. Although most static objects subtract cleanly, even a very low false positive detection rate can lead to hundreds of non-supernova candidates which must be vetted by human inspection before triggering additional followup. In comparison to simple threshold cuts, more sophisticated methods such as Boosted Decision Trees, Random Forests, and Support Vector Machines provide dramatically better object discrimination. At the Nearby Supernova Factory, we reduced the number of non-supernova candidates by a factor of 10 while increasing our supernova identification efficiency. Methods such as these will be crucial for maintaining a reasonable false positive rate in the automated transient alert pipelines of upcoming projects such as PanSTARRS and LSST.Comment: 25 pages; 6 figures; submitted to Ap

Modeling small objects under uncertainties : novel algorithms and applications.

Active Shape Models (ASM), Active Appearance Models (AAM) and Active Tensor Models (ATM) are common approaches to model elastic (deformable) objects. These models require an ensemble of shapes and textures, annotated by human experts, in order identify the model order and parameters. A candidate object may be represented by a weighted sum of basis generated by an optimization process. These methods have been very effective for modeling deformable objects in biomedical imaging, biometrics, computer vision and graphics. They have been tried mainly on objects with known features that are amenable to manual (expert) annotation. They have not been examined on objects with severe ambiguities to be uniquely characterized by experts. This dissertation presents a unified approach for modeling, detecting, segmenting and categorizing small objects under uncertainty, with focus on lung nodules that may appear in low dose CT (LDCT) scans of the human chest. The AAM, ASM and the ATM approaches are used for the first time on this application. A new formulation to object detection by template matching, as an energy optimization, is introduced. Nine similarity measures of matching have been quantitatively evaluated for detecting nodules less than 1 em in diameter. Statistical methods that combine intensity, shape and spatial interaction are examined for segmentation of small size objects. Extensions of the intensity model using the linear combination of Gaussians (LCG) approach are introduced, in order to estimate the number of modes in the LCG equation. The classical maximum a posteriori (MAP) segmentation approach has been adapted to handle segmentation of small size lung nodules that are randomly located in the lung tissue. A novel empirical approach has been devised to simultaneously detect and segment the lung nodules in LDCT scans. The level sets methods approach was also applied for lung nodule segmentation. A new formulation for the energy function controlling the level set propagation has been introduced taking into account the specific properties of the nodules. Finally, a novel approach for classification of the segmented nodules into categories has been introduced. Geometric object descriptors such as the SIFT, AS 1FT, SURF and LBP have been used for feature extraction and matching of small size lung nodules; the LBP has been found to be the most robust. Categorization implies classification of detected and segmented objects into classes or types. The object descriptors have been deployed in the detection step for false positive reduction, and in the categorization stage to assign a class and type for the nodules. The AAMI ASMI A TM models have been used for the categorization stage. The front-end processes of lung nodule modeling, detection, segmentation and classification/categorization are model-based and data-driven. This dissertation is the first attempt in the literature at creating an entirely model-based approach for lung nodule analysis

Comparing 3D descriptors for local search of craniofacial landmarks

This paper presents a comparison of local descriptors for a set of 26 craniofacial landmarks annotated on 144 scans acquired in the context of clinical research. We focus on the accuracy of the different descriptors on a per-landmark basis when constrained to a local search. For most descriptors, we find that the curves of expected error against the search radius have a plateau that can be used to characterize their performance, both in terms of accuracy and maximum usable range for the local search. Six histograms-based descriptors were evaluated: three describing distances and three describing orientations. No descriptor dominated over the rest and the best accuracy per landmark was strongly distributed among 3 of the 6 algorithms evaluated. Ordering the descriptors by average error (over all landmarks) did not coincide with the ordering by most frequently selected, indicating that a comparison of descriptors based on their global behavior might be misleading when targeting facial landmarks