Integral invariants for image enhancement

Medical images pose a major challenge for image analysis: often they have poor signal-to-noise, necessitating smoothing; yet such smoothing needs to preserve the boundaries of regions of interest and small features such as mammogram microcalcifications. We show how circular integral invariants (II) may be adapted for feature-preserving smoothing to facilitate segmentation. Though II is isotropic, we show that it leads to considerably less feature deterioration than Gaussian blurring and it improves segmentation of regions of interest as compared to anisotropic diffusion, particularly for hierarchical contour based segmentation methods

Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

Hand gesture recognition with jointly calibrated Leap Motion and depth sensor

Novel 3D acquisition devices like depth cameras and the Leap Motion have recently reached the market. Depth cameras allow to obtain a complete 3D description of the framed scene while the Leap Motion sensor is a device explicitly targeted for hand gesture recognition and provides only a limited set of relevant points. This paper shows how to jointly exploit the two types of sensors for accurate gesture recognition. An ad-hoc solution for the joint calibration of the two devices is firstly presented. Then a set of novel feature descriptors is introduced both for the Leap Motion and for depth data. Various schemes based on the distances of the hand samples from the centroid, on the curvature of the hand contour and on the convex hull of the hand shape are employed and the use of Leap Motion data to aid feature extraction is also considered. The proposed feature sets are fed to two different classifiers, one based on multi-class SVMs and one exploiting Random Forests. Different feature selection algorithms have also been tested in order to reduce the complexity of the approach. Experimental results show that a very high accuracy can be obtained from the proposed method. The current implementation is also able to run in real-time