Shape-constrained Gaussian process regression for surface reconstruction and multimodal, non-rigid image registration.

We present a new statistical framework for landmark ?>curve-based image registration and surface reconstruction. The proposed method first elastically aligns geometric features (continuous, parameterized curves) to compute local deformations, and then uses a Gaussian random field model to estimate the full deformation vector field as a spatial stochastic process on the entire surface or image domain. The statistical estimation is performed using two different methods: maximum likelihood and Bayesian inference via Markov Chain Monte Carlo sampling. The resulting deformations accurately match corresponding curve regions while also being sufficiently smooth over the entire domain. We present several qualitative and quantitative evaluations of the proposed method on both synthetic and real data. We apply our approach to two different tasks on real data: (1) multimodal medical image registration, and (2) anatomical and pottery surface reconstruction.

Efficacy of diffeomorphic surface matching and 3D geometric morphometrics for taxonomic discrimination of Early Pleistocene hominin mandibular molars.

Morphometric assessments of the dentition have played significant roles in hypotheses relating to taxonomic diversity among extinct hominins. In this regard, emphasis has been placed on the statistical appraisal of intraspecific variation to identify morphological criteria that convey maximum discriminatory power. Three-dimensional geometric morphometric (3D GM) approaches that utilize landmarks and semi-landmarks to quantify shape variation have enjoyed increasingly popular use over the past twenty-five years in assessments of the outer enamel surface (OES) and enamel-dentine junction (EDJ) of fossil molars. Recently developed diffeomorphic surface matching (DSM) methods that model the deformation between shapes have drastically reduced if not altogether eliminated potential methodological inconsistencies associated with the a priori identification of landmarks and delineation of semi-landmarks. As such, DSM has the potential to better capture the geometric details that describe tooth shape by accounting for both homologous and non-homologous (i.e., discrete) features, and permitting the statistical determination of geometric correspondence. We compare the discriminatory power of 3D GM and DSM in the evaluation of the OES and EDJ of mandibular permanent molars attributed to Australopithecus africanus, Paranthropus robustus and early Homo sp. from the sites of Sterkfontein and Swartkrans. For all three molars, classification and clustering scores demonstrate that DSM performs better at separating the A. africanus and P. robustus samples than does 3D GM. The EDJ provided the best results. P. robustus evinces greater morphological variability than A. africanus. The DSM assessment of the early Homo molar from Swartkrans reveals its distinctiveness from either australopith sample, and the "unknown" specimen from Sterkfontein (Stw 151) is notably more similar to Homo than to A. africanus.

Automatic detection and classification of manufacturing defects in metal boxes using deep neural networks.

This paper develops a new machine vision framework for efficient detection and classification of manufacturing defects in metal boxes. Previous techniques, which are based on either visual inspection or on hand-crafted features, are both inaccurate and time consuming. In this paper, we show that by using autoencoder deep neural network (DNN) architecture, we are able to not only classify manufacturing defects, but also localize them with high accuracy. Compared to traditional techniques, DNNs are able to learn, in a supervised manner, the visual features that achieve the best performance. Our experiments on a database of real images demonstrate that our approach overcomes the state-of-the-art while remaining computationally competitive.

Mapping and characterizing endometrial implants by registering 2D transvaginal ultrasound to 3D pelvic magnetic resonance images.

We propose a new deformable slice-to-volume registration method to register a 2D Transvaginal Ultrasound (TVUS) to a 3D Magnetic Resonance (MR) volume. Our main goal is to find a cross-section of the MR volume such that the endometrial implants and their depth of infiltration can be mapped from TVUS to MR. The proposed TVUS-MR registration method uses contour to surface correspondences through a novel variational one-step deformable Iterative Closest Point (ICP) method. Specifically, we find a smooth deformation field while establishing point correspondences automatically. We demonstrate the accuracy of the proposed method by quantitative and qualitative tests on both semi-synthetic and clinical data. To generate semi-synthetic data sets, 3D surfaces are deformed with 4-40% degrees of deformation and then various intersection curves are obtained at 0-20° cutting angles. Results show an average mean square error of 5.7934±0.4615mm, average Hausdorff distance of 2.493±0.14mm, and average Dice similarity coefficient of 0.9750±0.0030.

Elastic shape analysis of cylindrical surfaces for 3D/2D registration in endometrial tissue characterization.

We study the problem of joint registration and deformation analysis of endometrial tissue using 3D magnetic resonance imaging (MRI) and 2D trans-vaginal ultrasound (TVUS) measurements. In addition to the different imaging techniques involved in the two modalities, this problem is complicated due to: 1) different patient pose during MRI and TVUS observations, 2) the 3D nature of MRI and 2D nature of TVUS measurements, 3) the unknown intersecting plane for TVUS in MRI volume, and 4) the potential deformation of endometrial tissue during TVUS measurement process. Focusing on the shape of the tissue, we use expert manual segmentation of its boundaries in the two modalities and apply, with modification, recent developments in shape analysis of parametric surfaces to this problem. First, we extend the 2D TVUS curves to generalized cylindrical surfaces through replication, and then we compare them with MRI surfaces using elastic shape analysis. This shape analysis provides a simultaneous registration (optimal reparameterization) and deformation (geodesic) between any two parametrized surfaces. Specifically, it provides optimal curves on MRI surfaces that match with the original TVUS curves. This framework results in an accurate quantification and localization of the deformable endometrial cells for radiologists, and growth characterization for gynecologists and obstetricians. We present experimental results using semi-synthetic data and real data from patients to illustrate these ideas.

Three-dimensional face recognition using shapes of facial curves.

We study shapes of facial surfaces for the purpose of face recognition. The main idea is to 1) represent surfaces by unions of level curves, called facial curves, of the depth function and 2) compare shapes of surfaces implicitly using shapes of facial curves. The latter is performed using a differential geometric approach that computes geodesic lengths between closed curves on a shape manifold. These ideas are demonstrated using a nearest-neighbor classifier on two 3D face databases: Florida State University and Notre Dame, highlighting a good recognition performance.