Model-based learning of local image features for unsupervised texture segmentation

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images

Jump-sparse and sparse recovery using Potts functionals

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM). A series of experiments shows that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively. We highlight the capability of the method by comparing it with classical and recent approaches such as TV minimization (jump-sparse signals), orthogonal matching pursuit, iterative hard thresholding, and iteratively reweighted $\ell^1$ minimization (sparse signals)

Total variation regularization for manifold-valued data

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer

Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Exact algorithms for L1L^1-TV regularization of real-valued or circle-valued signals

We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper, we derive exact algorithms for both data spaces. A key ingredient is the reduction of the infinite search spaces to a finite set of configurations, which can be scanned by the Viterbi algorithm. To reduce the computational complexity of the involved tabulations, we extend the technique of distance transforms to non-uniform grids and to the circular data space. In total, the proposed algorithms have complexity $\mathscr{O}(KN)$ where $N$ is the length of the signal and $K$ is the number of different values in the data set. In particular, the complexity is $\mathscr{O}(N)$ for quantized data. It is the first exact algorithm for TV regularization with circle-valued data, and it is competitive with the state-of-the-art methods for scalar data, assuming that the latter are quantized

Motor deficits and recovery in rats with unilateral spinal cord hemisection mimic the Brown-Séquard syndrome

Cervical incomplete spinal cord injuries often lead to severe and persistent impairments of sensorimotor functions and are clinically the most frequent type of spinal cord injury. Understanding the motor impairments and the possible functional recovery of upper and lower extremities is of great importance. Animal models investigating motor dysfunction following cervical spinal cord injury are rare. We analysed the differential spontaneous recovery of fore- and hindlimb locomotion by detailed kinematic analysis in adult rats with unilateral C4/C5 hemisection, a lesion that leads to the Brown-Séquard syndrome in humans. The results showed disproportionately better performance of hindlimb compared with forelimb locomotion; hindlimb locomotion showed substantial recovery, whereas the ipsilesional forelimb remained in a very poor functional state. Such a differential motor recovery pattern is also known to occur in monkeys and in humans after similar spinal cord lesions. On the lesioned side, cortico-, rubro-, vestibulo- and reticulospinal tracts and the important modulatory serotonergic, dopaminergic and noradrenergic fibre systems were interrupted by the lesion. In an attempt to facilitate locomotion, different monoaminergic agonists were injected intrathecally. Injections of specific serotonergic and noradrenergic agonists in the chronic phase after the spinal cord lesion revealed remarkable, although mostly functionally negative, modulations of particular parameters of hindlimb locomotion. In contrast, forelimb locomotion was mostly unresponsive to these agonists. These results, therefore, show fundamental differences between fore- and hindlimb spinal motor circuitries and their functional dependence on remaining descending inputs and exogenous spinal excitation. Understanding these differences may help to develop future therapeutic strategies to improve upper and lower limb function in patients with incomplete cervical spinal cord injurie

The L1-Potts functional for robust jump-sparse reconstruction

We investigate the non-smooth and non-convex $L^1$-Potts functional in discrete and continuous time. We show $\Gamma$-convergence of discrete $L^1$-Potts functionals towards their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete $L^1$-Potts problem, we introduce an $O(n^2)$ time and $O(n)$ space algorithm to compute an exact minimizer. We apply $L^1$-Potts minimization to the problem of recovering piecewise constant signals from noisy measurements $f.$ It turns out that the $L^1$-Potts functional has a quite interesting blind deconvolution property. In fact, we show that mildly blurred jump-sparse signals are reconstructed by minimizing the $L^1$-Potts functional. Furthermore, for strongly blurred signals and known blurring operator, we derive an iterative reconstruction algorithm

Negative emotions influence how we move the computer mouse

Finding offers game-changing options for businesses, insider-threat detection and national security, write Martin Hibbeln, Jeffrey Jenkins, Christoph Schneider, Joe Valacich and Markus Weinman