Chen Sagiv

Integrated active contours for texture segmentation

We address the issue of textured image segmentation in the context of the Gabor feature space of images. Gabor filters tuned to a set of orientations, scales and frequencies are applied to the images to create the Gabor feature space. A two-dimensional Riemannian manifold of local features is extracted via the Beltrami framework. The metric of this surface provides a good indicator of texture changes and is used, therefore, in a Beltrami-based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation. The performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation. Moreover, an integrated approach, extending the geodesic and edgeless active contours approaches to texture segmentation, is presented. We show that combining boundary and region information yields more robust and accurate texture segmentation results.

THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM

Finding optimal representations of signals in higher dimensions, in particular directional representations, is currently the subject of intensive research. Since the classical wavelet transform does not provide precise directional information in the sense of resolving the wavefront set, several new representation systems were proposed in the past, including ridgelets, curvelets and, more recently, Shearlets. In this paper we study and visualize the continuous Shearlet transform. Moreover, we aim at deriving mother Shearlet functions which ensure optimal accuracy of the parameters of the associated transform. For this, we first show that this transform is associated with a unitary group representation coming from the so-called Shearlet group and compute the associated admissibility condition. This enables us to employ the general uncertainty principle in order to derive mother Shearlet functions that minimize the uncertainty relations derived for the infinitesimal generators of the Shearlet group: scaling, shear and translations. We further discuss methods to ensure square-integrability of the derived minimizers by considering weighted L2-spaces. Moreover, we study whether the minimizers satisfy the admissibility condition, thereby proposing a method to balance between the minimizing and the admissibility property.

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups.This study is concerned with the uncertainty principle in the context of the Weyl-Heisenberg, the SIM(2), the Affine and the Affine-Weyl-Heisenberg groups. We explore the relationship between the two-dimensional affine group and the SIM (2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scale-space properties of some of the minimizers are explored.

Fetal autonomic nervous system activity monitoring by spectral analysis of heart rate variations

Using an accurate beat-to-beat detection algorithm for fetal heart rate (FHR) from abdominal electrocardiograms (ECGs) and spectral analysis of heart rate fluctuations, with simultaneous recording of fetal breathing movements (FBMs) by ultrasound imaging, the authors were able to display the continuous activity of the fetal autonomic nervous system (ANS). The continuous display of fetal ANS activity presented may offer an adequate tool for the evaluation of fetal viability. FHR and FBM can be measured by a single procedure. The method provides FHR and FBM as estimated by the power of HR fluctuations reflecting ANS activity in the frequency band related to FBM. Thus, two complementary indications of the fetal viability are obtained simultaneously, from a single noninvasive measurement which allows continuous time dependent monitoring.<<ETX>>

Gabor-Space Geodesic Active Contours

A novel scheme for texture segmentation is presented. Our algorithm is based on generalizing the intensity-based geodesic active contours model to the Gabor spatial-feature space of images. First, we apply the Gabor-Morlet transform to the image using self similar Gabor functions, and then implement the geodesic active snakes mechanism in this space. The spatial-feature space is represented, via the Beltrami framework, as a Riemannian manifold. The stopping term, in the geodesic snake mechanism, is generalized and is derived from the metric of the Gabor spatial-feature manifold. Experimental results obtained by applying the scheme to test images are presented.

Application of a semiautomatic boundary detection algorithm for the assessment of amniotic fluid quantity from ultrasound images

The aim of this study was to develop a computer-assisted method to evaluate amniotic fluid volume (AFV). This was done by automatically detecting the boundaries of the amniotic fluid portion in 2-D ultrasonographic images. The study population consisted of 36 low-risk patients that were selected at random from a healthy population undergoing routine pregnancy follow-up. For each patient, images of the four quadrants of the uterus were digitized into a PC. The amniotic fluid portion in each ultrasonographic image was automatically detected, and its area was calculated. Its area was also manually determined by an expert physician (R. T.). The areas automatically detected by the algorithm were highly correlated with the areas manually delimited by the expert: r2 = 0.9722 (p < 0.01). The areas calculated by the program provide a good measure for the areas determined by the expert and may, therefore, be used for calculating the actual amniotic fluid volume.

StereographicCombing a Porcupine or Studies on Direction Diffusion in Image Processing

This paper addresses the problem of feature enhancement in noisy images when the feature is known to be constrained to a manifold. As an example, we approach the direction denoising problem in a general dimension via the geometric Beltrami framework for image processing. The spatial-direction space is a fiber bundle in which the spatial part is the base manifold and the direction space is the fiber. The feature (direction) field is represented accordingly as a section of the spatial-feature fiber bundle. The resulting Beltrami flow is a selective smoothing process that respects the bundles structure, i.e., the feature constraint. Direction diffusion is treated as a canonical example of a non-Euclidean feature space. The structures of the fiber spaces of interest in this paper are the unit circle S1 , the unit sphere S2 , and the unit hypersphere Sn. Applications to color analysis are discussed, and numerical experiments demonstrate again the benefits of the Beltrami framework in comparison to other featu...

Numerical experiments with MALDI Imaging data

This article does not present new mathematical results, it solely aims at discussing some numerical experiments with MALDI Imaging data. However, these experiments are based on and could not be done without the mathematical results obtained in the UNLocX project. They tackle two obstacles which presently prevent clinical routine applications of MALDI Imaging technology. In the last decade, matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) has developed into a powerful bioanalytical imaging modality. MALDI imaging data consists of a set of mass spectra, which are measured at different locations of a flat tissue sample. Hence, this technology is capable of revealing the full metabolic structure of the sample under investigation. Sampling resolution as well as spectral resolution is constantly increasing, presently a conventional 2D MALDI Imaging data requires up to 100 GB per dataset. A major challenge towards routine applications of MALDI Imaging in pharmaceutical or medical workflows is the high computational cost for evaluating and visualizing the information content of MALDI imaging data. This becomes even more critical in the near future when considering cohorts or 3D applications. Due to its size and complexity MALDI Imaging constitutes a challenging test case for high performance signal processing. In this article we will apply concepts and algorithms, which were developed within the UNLocX project, to MALDI Imaging data. In particular we will discuss a suitable phase space model for such data and report on implementations of the resulting transform coders using GPU technology. Within the MALDI Imaging workflow this leads to an efficient baseline removal and peak picking. The final goal of data processing in MALDI Imaging is the discrimination of regions having different metabolic structures. We introduce and discuss so-called soft-segmentation maps which are obtained by non-negative matrix factorization incorporating sparsity constraints.

Scale-space generation via uncertainty principles

This study is concerned with the uncertainty principles which are related to the Weyl-Heisenberg, the SIM(2) and the Affine groups. A general theorem which associates an uncertainty principle to a pair of self-adjoint operators was previously used in finding the minimizers of the uncertainty principles related to various groups, e.g., the one and two-dimensional Weyl-Heisenberg groups, the one-dimensional Affine group, and the two-dimensional similitude group of ℝ2, SIM(2) = ℝ2 ×(ℝ+ × SO(2)). In this study the relationship between the affine group in two dimensions and the SIM(2) group is investigated in terms of the uncertainty minimizers. Moreover, we present scale space properties of a minimizer of the SIM(2) group.

Signal representation, uncertainty principles and localization measures

The following collection of articles addresses one of the most basic problems in signal and image processing, namly the search for function systems (basis, frames, dictionaries) which allow efficient representations of certain classes of signals/images. Such representations are essential for decomposition and synthesis of signals, hence they are at the core of almost any application (coding, compression, pattern matching, feature extraction, classification, etc.) in this field. Accordingly, this is one of the best-studied topics in data analysis and a multitude of different concepts also addressing discretization/algorithmic issues has been investigated in this context. The starting point for reviving activities in this field was a recently rediscovered inconsistency in the concept of constructing optimally localized basis functions by minimizing uncertainty principles. In this short introductory note, we shortly sketch the basic dilemma, which was the starting point for this research approximately three years ago. However, the subsequent investigations presented in this collection of papers cover a much wider range of more general localization measures, discretization concepts as well as discussing algorithmic efficiency and stability.