Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size

On The Continuous Steering of the Scale of Tight Wavelet Frames

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the "scale" of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication

Principled Design and Implementation of Steerable Detectors

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown position and orientation. We propose a continuous-domain additive image model, where the analyzed image is the sum of the template and an isotropic background signal with self-similar isotropic power-spectrum. The method is able to learn an optimal steerable filter fulfilling the SNR criterion based on one single template and background pair, that therefore strongly responds to the template, while optimally decoupling from the background model. The proposed filter then allows for a fast detection process, with the unknown orientation estimation through the use of steerability properties. In practice, the implementation requires to discretize the continuous-domain formulation on polar grids, which is performed using radial B-splines. We demonstrate the practical usefulness of our method on a variety of template approximation and pattern detection experiments

Még egy csepp interakció = One More Drop of Interaction

A hypertoniás betegek terápiájának összeállítása különösen nagy odafigyelést igényel. A hypertonia stádiumbeosztása, a társbetegségek és szövődmények mellett figyelembe kell venni az egyidejűleg alkalmazott gyógyszerek és gyógyhatású szerek között fellépő kölcsönhatásokat is. A közleményben a szerzők bemutatnak egy beteget, aki a hypertonia-ambulancián történt sikeres gyógyszerbeállítást követően normotenzívvé vált, majd néhány hónap múlva hypotoniás epizódok által okozott szédülés, valamint hasmenés miatt jelentkezett újabb kontrollra. Ennek kapcsán a hypertonia-ambulancián derült fény a beteg által elkezdett kannabiszolaj hatóanyagának, a kannabidiolnak a kölcsönhatásaira az antihipertenzív és antidiabetikus, valamint gyomorsavszekréció-gátló szerekkel. A szerzők felhívják a figyelmet arra, hogy a betegek által fogyasztott táplálékkiegészítők sem mindig veszélytelenek, és a hirtelen fellépő, megmagyarázhatatlan panaszok hátterében mindig kell gyógyszerkölcsönhatások után is kutatni. A közleményben a fenti konkrét eset kapcsán kerülnek áttekintésre a kannabidioltartalmú étrend-kiegészítők hatásmechanizmusával, lehetséges mellékhatásaival és gyógyszerkölcsönhatásaival kapcsolatos, a gyakorló orvos számára legfontosabb ismeretek. The composition of hypertensive patients’ therapy requires particular attention. Beside the classification of hypertension, the co-morbidities and the complications, the interactions between the simultaneously applied medications and medical products should be considered. In the publication the authors present a patient, who became normotensive after a successful therapy optimalization at the hypertension outpatient clinic, and then after a few month applied for check-up due to dizziness caused by hypotensive episodes and diarrhoea. In connection with this the interaction of the cannabidiol, the active compound of cannabis oil, which was taken by the patient, came to light, as well as the side effects in connection with the antihypertensive, antidiabetic, and gastric acid secretion inhibitor drugs. The authors draw attention to the fact that the dietary supplements taken by the patients are not always harmless, and in case of sudden onset, inexplicable complaints, drug interaction should be investigated in the background. In the publication, an overview of the most important knowledge for the practicing physician is provided about the mechanism of action, possible side effects and drug interactions of the cannabidiol containing dietary supplement

SpotCaliper: fast wavelet-based spot detection with accurate size estimation

Motivation: SpotCaliper is a novel wavelet-based image-analysis software providing a fast automatic detection scheme for circular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a friendly user interface. The user is allowed to edit the results by modifying the measurements (in a semi-automated way), extract data for further analysis. The fine tuning of the detections includes the possibility of adjusting or removing the original detections, as well as adding further spots. Results: The main advantage of the software is its ability to capture the size of spots in a fast and accurate way. Availability and implementation: http://bigwww.epfl.ch/algorithms/spotcaliper/ Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online

On The Continuous Steering Of The Scale Of Tight Wavelet Frames

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be “dilated” by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the “scale” of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication

Method and system for the creation of an h-spline based data structure, data storage, and data representation

A method for generating a data structure to digitally represent a geometrical object based on H-splines, the method being performed on a computer device having a data processor and memory, the method including the steps of creating a first data structure and storing a plurality of control points and higher order derivatives that define the geometrical object in a parameter domain using the H-splines in the first data structure of the memory, creating a second data structure and storing coordinate data that define the geometrical object as a coordinate data model in the second data structure of the memory, and creating and storing a connectivity array in the memory that links the plurality of control points of the parameter domain to the coordinate data of the coordinate data model

System and method for performing isogeometric analysis and finite element analysis using h-splines

A method for performing H-spline compatible isogeometric analysis (IGA) on a geometric object, the method being performed on a computer device having a memory, the method including the steps of creating an analysis suitable geometry (ASG) using H-splines from the geometric object, the geometric object being represented by H-splines, storing the analysis suitable geometry (ASG) in the memory, and performing the H-spline compatible IGA on the ASG stored in the memory of the computer device to generate the data the represents a stiffness matrix and a force vector of the H-spline compatible IGA

Spotcaliper: Fast Wavelet-Based Spot Detection With Accurate Size Estimation

Motivation: SpotCaliper is a novel wavelet-based image-analysis software providing a fast automatic detection scheme for circular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a friendly user interface. The user is allowed to edit the results by modifying the measurements (in a semi-automated way), extract data for further analysis. The fine tuning of the detections includes the possibility of adjusting or removing the original detections, as well as adding further spots. Results: The main advantage of the software is its ability to capture the size of spots in a fast and accurate way

Transforms and Operators for Directional Bioimage Analysis: A Survey

We give a methodology-oriented perspective on directional image analysis and rotation-invariant processing. We review the state of the art in the field and make connections with recent mathematical developments in functional analysis and wavelet theory. We unify our perspective within a common framework using operators. The intent is to provide image-processing methods that can be deployed in algorithms that analyze biomedical images with improved rotation invariance and high directional sensitivity. We start our survey with classical methods such as directional-gradient and the structure tensor. Then, we discuss how these methods can be improved with respect to robustness, invariance to geometric transformations (with a particular interest in scaling), and computation cost. To address robustness against noise, we move forward to higher degrees of directional selectivity and discuss Hessian-based detection schemes. To present multiscale approaches, we explain the differences between Fourier filters, directional wavelets, curvelets, and shearlets. To reduce the computational cost, we address the problem of matching directional patterns by proposing steerable filters, where one might perform arbitrary rotations and optimizations without discretizing the orientation. We define the property of steerability and give an introduction to the design of steerable filters. We cover the spectrum from simple steerable filters through pyramid schemes up to steerable wavelets. We also present illustrations on the design of steerable wavelets and their application to pattern recognition