On Invariance, Equivariance, Correlation and Convolution of Spherical Harmonic Representations for Scalar and Vectorial Data

The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation and practical implementation of SH representations, summarizing works on rotation invariant and equivariant features, as well as convolutions and exact correlations of signals on spheres. In extension, these methods are then generalized from scalar SH representations to Vectorial Harmonics (VH), providing the same capabilities for 3d vector fields on spheresComment: 106 pages, tech repor

Biological image analysis

In biological research images are extensively used to monitor growth, dynamics and changes in biological specimen, such as cells or plants. Many of these images are used solely for observation or are manually annotated by an expert. In this dissertation we discuss several methods to automate the annotating and analysis of bio-images. Two large clusters of methods have been investigated and developed. A first set of methods focuses on the automatic delineation of relevant objects in bio-images, such as individual cells in microscopic images. Since these methods should be useful for many different applications, e.g. to detect and delineate different objects (cells, plants, leafs, ...) in different types of images (different types of microscopes, regular colour photographs, ...), the methods should be easy to adjust. Therefore we developed a methodology relying on probability theory, where all required parameters can easily be estimated by a biologist, without requiring any knowledge on the techniques used in the actual software. A second cluster of investigated techniques focuses on the analysis of shapes. By defining new features that describe shapes, we are able to automatically classify shapes, retrieve similar shapes from a database and even analyse how an object deforms through time

On Improving Generalization of CNN-Based Image Classification with Delineation Maps Using the CORF Push-Pull Inhibition Operator

Deployed image classification pipelines are typically dependent on the images captured in real-world environments. This means that images might be affected by different sources of perturbations (e.g. sensor noise in low-light environments). The main challenge arises by the fact that image quality directly impacts the reliability and consistency of classification tasks. This challenge has, hence, attracted wide interest within the computer vision communities. We propose a transformation step that attempts to enhance the generalization ability of CNN models in the presence of unseen noise in the test set. Concretely, the delineation maps of given images are determined using the CORF push-pull inhibition operator. Such an operation transforms an input image into a space that is more robust to noise before being processed by a CNN. We evaluated our approach on the Fashion MNIST data set with an AlexNet model. It turned out that the proposed CORF-augmented pipeline achieved comparable results on noise-free images to those of a conventional AlexNet classification model without CORF delineation maps, but it consistently achieved significantly superior performance on test images perturbed with different levels of Gaussian and uniform noise

Machine learning methods for discriminating natural targets in seabed imagery

The research in this thesis concerns feature-based machine learning processes and methods for discriminating qualitative natural targets in seabed imagery. The applications considered, typically involve time-consuming manual processing stages in an industrial setting. An aim of the research is to facilitate a means of assisting human analysts by expediting the tedious interpretative tasks, using machine methods. Some novel approaches are devised and investigated for solving the application problems. These investigations are compartmentalised in four coherent case studies linked by common underlying technical themes and methods. The first study addresses pockmark discrimination in a digital bathymetry model. Manual identification and mapping of even a relatively small number of these landform objects is an expensive process. A novel, supervised machine learning approach to automating the task is presented. The process maps the boundaries of ≈ 2000 pockmarks in seconds - a task that would take days for a human analyst to complete. The second case study investigates different feature creation methods for automatically discriminating sidescan sonar image textures characteristic of Sabellaria spinulosa colonisation. Results from a comparison of several textural feature creation methods on sonar waterfall imagery show that Gabor filter banks yield some of the best results. A further empirical investigation into the filter bank features created on sonar mosaic imagery leads to the identification of a useful configuration and filter parameter ranges for discriminating the target textures in the imagery. Feature saliency estimation is a vital stage in the machine process. Case study three concerns distance measures for the evaluation and ranking of features on sonar imagery. Two novel consensus methods for creating a more robust ranking are proposed. Experimental results show that the consensus methods can improve robustness over a range of feature parameterisations and various seabed texture classification tasks. The final case study is more qualitative in nature and brings together a number of ideas, applied to the classification of target regions in real-world sonar mosaic imagery. A number of technical challenges arose and these were surmounted by devising a novel, hybrid unsupervised method. This fully automated machine approach was compared with a supervised approach in an application to the problem of image-based sediment type discrimination. The hybrid unsupervised method produces a plausible class map in a few minutes of processing time. It is concluded that the versatile, novel process should be generalisable to the discrimination of other subjective natural targets in real-world seabed imagery, such as Sabellaria textures and pockmarks (with appropriate features and feature tuning.) Further, the full automation of pockmark and Sabellaria discrimination is feasible within this framework

MC 2019 Berlin Microscopy Conference - Abstracts

Das Dokument enthält die Kurzfassungen der Beiträge aller Teilnehmer an der Mikroskopiekonferenz "MC 2019", die vom 01. bis 05.09.2019, in Berlin stattfand

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Towards a circular economy: fabrication and characterization of biodegradable plates from sugarcane waste

Bagasse pulp is a promising material to produce biodegradable plates. Bagasse is the fibrous residue that remains after sugarcane stalks are crushed to extract their juice. It is a renewable resource and is widely available in many countries, making it an attractive alternative to traditional plastic plates. Recent research has shown that biodegradable plates made from Bagasse pulp have several advantages over traditional plastic plates. For example, they are more environmentally friendly because they are made from renewable resources and can be composted after use. Additionally, they are safer for human health because they do not contain harmful chemicals that can leach into food. The production process for Bagasse pulp plates is also relatively simple and cost-effective. Bagasse is first collected and then processed to remove impurities and extract the pulp. The pulp is then molded into the desired shape and dried to form a sturdy plate. Overall, biodegradable plates made from Bagasse pulp are a promising alternative to traditional plastic plates. They are environmentally friendly, safe for human health, and cost-effective to produce. As such, they have the potential to play an important role in reducing plastic waste and promoting sustainable practices. Over the years, the world was not paying strict attention to the impact of rapid growth in plastic use. As a result, uncontrollable volumes of plastic garbage have been released into the environment. Half of all plastic garbage generated worldwide is made up of packaging materials. The purpose of this article is to offer an alternative by creating bioplastic goods that can be produced in various shapes and sizes across various sectors, including food packaging, single-use tableware, and crafts. Products made from bagasse help address the issue of plastic pollution. To find the optimum option for creating bagasse-based biodegradable dinnerware in Egypt and throughout the world, researchers tested various scenarios. The findings show that bagasse pulp may replace plastics in biodegradable packaging. As a result of this value-added utilization of natural fibers, less waste and less of it ends up in landfills. The practical significance of this study is to help advance low-carbon economic solutions and to produce secure bioplastic materials that can replace Styrofoam in tableware and food packaging production