Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Face recognition technologies for evidential evaluation of video traces

Human recognition from video traces is an important task in forensic investigations and evidence evaluations. Compared with other biometric traits, face is one of the most popularly used modalities for human recognition due to the fact that its collection is non-intrusive and requires less cooperation from the subjects. Moreover, face images taken at a long distance can still provide reasonable resolution, while most biometric modalities, such as iris and fingerprint, do not have this merit. In this chapter, we discuss automatic face recognition technologies for evidential evaluations of video traces. We first introduce the general concepts in both forensic and automatic face recognition , then analyse the difficulties in face recognition from videos . We summarise and categorise the approaches for handling different uncontrollable factors in difficult recognition conditions. Finally we discuss some challenges and trends in face recognition research in both forensics and biometrics . Given its merits tested in many deployed systems and great potential in other emerging applications, considerable research and development efforts are expected to be devoted in face recognition in the near future

The Parameter-Less Self-Organizing Map algorithm

The Parameter-Less Self-Organizing Map (PLSOM) is a new neural network algorithm based on the Self-Organizing Map (SOM). It eliminates the need for a learning rate and annealing schemes for learning rate and neighbourhood size. We discuss the relative performance of the PLSOM and the SOM and demonstrate some tasks in which the SOM fails but the PLSOM performs satisfactory. Finally we discuss some example applications of the PLSOM and present a proof of ordering under certain limited conditions.Comment: 29 pages, 27 figures. Based on publication in IEEE Trans. on Neural Network

Model Transport: Towards Scalable Transfer Learning on Manifolds

We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer from an obvious shortcoming: Transporting large datasets is prohibitively expensive, hindering scalability. Fortunately, with our approach, we never transport data. Rather, we show how the statistical models themselves can be transported, and prove that for the tangent-space models above, the transport “commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image descriptors

Deep Directional Statistics: Pose Estimation with Uncertainty Quantification

Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low-resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty in order to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper, we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art