Minimax Geometric Fitting of Two Corresponding Sets of Points and Dynamic Furthest Voronoi Diagrams

This paper formulates problems of fitting two corresponding sets of points by translation, rotation and scaling, and proposes efficient algorithms for the fitting. The algorithms are based on the theory of lower envelopes, or Davenport-Schinzel sequences, and linearization techniques in computational geometry, and are related to dynamic furthest Voronoi diagrams.PAPE

GAGAN: Geometry-Aware Generative Adversarial Networks

Deep generative models learned through adversarial training have become increasingly popular for their ability to generate naturalistic image textures. However, aside from their texture, the visual appearance of objects is significantly influenced by their shape geometry; information which is not taken into account by existing generative models. This paper introduces the Geometry-Aware Generative Adversarial Networks (GAGAN) for incorporating geometric information into the image generation process. Specifically, in GAGAN the generator samples latent variables from the probability space of a statistical shape model. By mapping the output of the generator to a canonical coordinate frame through a differentiable geometric transformation, we enforce the geometry of the objects and add an implicit connection from the prior to the generated object. Experimental results on face generation indicate that the GAGAN can generate realistic images of faces with arbitrary facial attributes such as facial expression, pose, and morphology, that are of better quality than current GAN-based methods. Our method can be used to augment any existing GAN architecture and improve the quality of the images generated

Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

Recent studies show that asymmetric sigmoidal response curves are not uncommonin biomedical studies. For example, the 5-parameter logistic (5PL) model isfrequently used to model and analyze responses from bioassays and immunoassayswhich can be skewed. Various types of optimal experimental designs for 2, 3 and4-parameter logistic models have been reported but not for the more complicated5-parameter logistic (5PL) model. Designs currently used for the 5PL model seemad-hoc with no formal quantitative assessment of their efficiencies. We constructdifferent types of optimal designs for studying various features of the 5PL modeland use them to evaluate efficiencies of commonly used designs in bioassays andimmunoassays. We also create a user-friendly software package to search for optimaldesigns tailor-made to user-specified problems for the 5PL model and evaluaterobustness properties of the design under a variation of criteria, model formsand mis-specification in the nominal values of the model parameters. Our designstrategies can also account for several objectives with varying degrees of importance.As an application, we generate optimal designs for the 5PL model for real studiesin immunoassays and bioassays, and show currently used designs are generallyinefficient for statistical inference

A Comparison of Multi-instance Learning Algorithms

Motivated by various challenging real-world applications, such as drug activity prediction and image retrieval, multi-instance (MI) learning has attracted considerable interest in recent years. Compared with standard supervised learning, the MI learning task is more difficult as the label information of each training example is incomplete. Many MI algorithms have been proposed. Some of them are specifically designed for MI problems whereas others have been upgraded or adapted from standard single-instance learning algorithms. Most algorithms have been evaluated on only one or two benchmark datasets, and there is a lack of systematic comparisons of MI learning algorithms. This thesis presents a comprehensive study of MI learning algorithms that aims to compare their performance and find a suitable way to properly address different MI problems. First, it briefly reviews the history of research on MI learning. Then it discusses five general classes of MI approaches that cover a total of 16 MI algorithms. After that, it presents empirical results for these algorithms that were obtained from 15 datasets which involve five different real-world application domains. Finally, some conclusions are drawn from these results: (1) applying suitable standard single-instance learners to MI problems can often generate the best result on the datasets that were tested, (2) algorithms exploiting the standard asymmetric MI assumption do not show significant advantages over approaches using the so-called collective assumption, and (3) different MI approaches are suitable for different application domains, and no MI algorithm works best on all MI problems