Optimization of Surface Registrations Using Beltrami Holomorphic Flow

Landmark constrained genus-one surface Teichmüller map applied to surface registration in medical imaging.

Three-dimensional Feature Recognition-based Automated Patient Treatment Mismatch Verification System for Radiation Therapy

There is a growing interest in shape analysis in recent years. We present a novel shape signature for 2D bounded simply-connected domains, named the Harmonic Beltrami signature (HBS). The proposed signature is based on the harmonic extension of the conformal welding map of a unit circle and its Beltrami coefficient. We show that there is a one-to-one correspondence between the quotient space of HBS and the space of 2D simply-connected shapes up to a translation, rotation and scaling. With a suitable normalization, each equivalence class in the quotient space of HBS is associated to a unique representative. It gets rid of the conformal ambiguity. As such, each shape is associated to a unique HBS. Conversely, the associated shape of a HBS can be reconstructed based on quasiconformal Teichmuller theories, which is uniquely determined up to a translation, rotation and scaling. The HBS is thus an effective fingerprint to represent a 2D shape. The robustness of HBS is studied both theoretically and experimentally. With the HBS, simple metric, such as L2, can be used to measure geometric dissimilarity between shapes. Experiments have been carried out to classify shapes in different classes using HBS. Results show good classification performance, which demonstrate the efficacy of our proposed shape signature.

We consider problems concerning the existence of solutions of the Beltrami equations and their convergence in the complex plane. We are mainly interested in the case when these solutions satisfy the so-called hydrodynamic normalization condition in the neighborhood of infinity. Under some conditions on dilatations of inverse mappings, we have established the existence of such solutions in the class of continuous Sobolev mappings. We have also obtained results on the locally uniform limit of a sequence of such solutions.

This paper presents a novel technique for hand shape and appearance based personal identification and verification. It has two major building blocks. A segmentation block presents robust and fully automatic algorithms which are able to accurately segment the hand's palm and fingers irrespective of colour contrast between the fosreground and background. They achieve a consistent representation of the fingers and the palm regardless of their pose/orientation or the spaces between the fingers. In the feature extraction/matching block, the iterative closest point (ICP) algorithm is employed to align the images. Both shape and appearance based features are extracted and comparatively assessed. The modified Hausdorff distance and independent component analysis (ICA) algorithms are used for shape and appearance analysis. Identification and verification were performed using fusion strategies upon the similarity scores of the fingers and the palm. Experimental results show the proposed system exhibits an accuracy of over 98% in hand recognition and verification in a database consisting of 500 different subjects.

Asymptotic analysis for proximal-type methods in vector variational inequality problems

Nonlocal variational theory and optimal control problems

Hexamethoxymethylmelamine, a common crosslinker used in combination with polyester resins to prepare thermosetting coatings, can self-condense during curing and in theory build up regions with high crosslink density (melamine enrichment). This distribution may affect such properties as the “local” glass transition temperature and structural heterogeneity and thereby modify formability, stain resistance, and weatherability. The self-condensation regions have not previously been observed in detail so their distribution in the film is unclear. Confocal Raman microscopy (CRM) has been used to characterize the melamine distribution in three polyester–melamine paint systems: one clear and two pigmented coil coatings. Both the surface mapping and depth profiling features of CRM were used to perform a 3D analysis. The depth profiling of the clear coating was performed in a nondestructive way, but due to the opaque nature of the pigments, cross sections of the pigmented coatings were prepared in order to facilitate the analysis of the melamine distribution through the film thickness. Melamine-enriched zones were found on the surfaces of all three samples. They appeared to be approximately spherical with diameters of around 5 μm. It was also observed from the cross sections that the melamine-enriched zones appeared as “particles” distributed randomly through the coating. The Raman spectra collected at these regions show significantly higher triazine ring band intensity. All of these findings confirm the hypotheses constructed over the past 20–30 years.

This paper introduces a general setting for the construction of data fidelity metrics between oriented or non-oriented geometric shapes like curves, curve sets or surfaces. These metrics are based on the representation of shapes as distributions of their local tangent or normal vectors and the definition of reproducing kernels on these spaces. The construction, that combines in one common setting and extends the previous frameworks of currents and varifolds, provides a very large class of kernel metrics which can be easily computed without requiring any kind of parametrization of shapes and which are smooth enough to give robustness to certain imperfections that could result e.g. from bad segmentation. We then give a sense, with synthetic examples, of the versatility and potentialities of such metrics when used in various problems like shape comparison, clustering and diffeomorphic registration.

Many applied problems can be understood and solved in terms of the minimization of a functional, usually related to the energy, in an appropriate functional space. Minimization and variational problems are at the interface between nonlinear analysis, calculus of variations, differential equations, and mathematical physics and play a fundamental role in the application of mathematics to real-world problems.

In this work, we aim to advance the traditional approach to 3D object classification for its lighter computation and memory costs than the deep learning based approach. Specifically, we propose a novel algorithm that uses multiple handcrafted descriptors to characterize the 3D surface and its multi-view 2D projections, pairs each descriptor with a base classifier and applies AdaBoost to derive the final classifier. In the proposed algorithm, simple yet effective descriptors are selected or designed for lightweight construction, and shape analyses are made on multiple scales of the 2D projections and integrated for the final classification. Experiments show that the proposed algorithm achieves significantly higher accuracy and efficiency than the benchmark traditional methods. Experiments also show that, compared with the state-of-the-art benchmark deep learning based methods, the proposed algorithm wins sharply in efficiency though sacrificing the accuracy by several percent.

Light Detection and Ranging (LiDAR)-based simultaneous localization and mapping (SLAM) is a core technology for autonomous vehicles and robots. One key contribution of this work to 3D LiDAR SLAM and localization is a fierce defense of view-based maps (pose graphs with time-stamped sensor readings) as the fundamental representation of maps. As will be shown, they allow for the greatest flexibility, enabling the posterior generation of arbitrary metric maps optimized for particular tasks, for example, obstacle avoidance and real-time localization. Moreover, this work introduces a new framework in which mapping pipelines can be defined without coding, defining the connections of a network of reusable blocks much like deep-learning networks are designed by connecting layers of standardized elements. We also introduce tightly-coupled estimation of linear and angular velocity vectors within the Iterative Closest Point (ICP)-like optimizer, leading to superior robustness against aggressive motion profiles without the need for an IMU. Extensive experimental validation reveals that the proposal compares well to, or improves, former state-of-the-art (SOTA) LiDAR odometry systems, while also successfully mapping some hard sequences where others diverge. A proposed self-adaptive configuration has been used, without parameter changes, for all 3D LiDAR datasets with sensors between 16 and 128 rings, and has been extensively tested on 83 sequences over more than 250 km of automotive, hand-held, airborne, and quadruped LiDAR datasets, both indoors and outdoors. The system flexibility is demonstrated with additional configurations for 2D LiDARs and for building 3D NDT-like maps. The framework is open-sourced online: https://github.com/MOLAorg/mola.

Self-organisation can generate the discontinuities in the somatosensory map

Classifying isolated vertebrate bones to a high level of taxonomic precision can be difficult. Many of Australia’s Cretaceous terrestrial vertebrate fossil-bearing deposits, for example, produce large numbers of isolated bones and very few associated or articulated skeletons. Identifying these often fragmentary remains beyond high-level taxonomic ranks, such as Ornithopoda or Theropoda, is difficult and those classified to lower taxonomic levels are often debated. The ever-increasing accessibility to 3D-based comparative techniques has allowed palaeontologists to undertake a variety of shape analyses, such as geometric morphometrics, that although powerful and often ideal, require the recognition of diagnostic landmarks and the generation of sufficiently large data sets to detect clusters and accurately describe major components of morphological variation. As a result, such approaches are often outside the scope of basic palaeontological research that aims to simply identify fragmentary specimens. Herein we present a workflow in which pairwise comparisons between fragmentary fossils and better known exemplars are digitally achieved through three-dimensional mapping of their surface profiles and the iterative closest point (ICP) algorithm. To showcase this methodology, we compared a fragmentary theropod ungual (NMV P186153) from Victoria, Australia, identified as a neovenatorid, with the manual unguals of the megaraptoran Australovenator wintonensis (AODF604). We discovered that NMV P186153 was a near identical match to AODF604 manual ungual II-3, differing only in size, which, given their 10–15Ma age difference, suggests stasis in megaraptoran ungual morphology throughout this interval. Although useful, our approach is not free of subjectivity; care must be taken to eliminate the effects of broken and incomplete surfaces and identify the human errors incurred during scaling, such as through replication. Nevertheless, this approach will help to evaluate and identify fragmentary remains, adding a quantitative perspective to an otherwise qualitative endeavour.

In this paper we study laminar currents in ℙ2. Given a sequence of irreducible algebraic curves (C n ) converging in the sense of currents to T, we find geometric conditions on the curves ensuring that the limit current T is laminar. This criterion is then applied to meromorphic dynamical systems in ℙ2, and laminarity of the dynamical ``Green'' current is obtained for a wide class of meromorphic self maps of ℙ2, as well as for all bimeromorphic maps of projective surfaces.