image elements are covered by the imaged components. The model is useful for improving information extraction from digital images and reducing problems originating from limited spatial resolution. We have by now developed methods for estimation of a number of features of coverage representation of shapes and demonstrated their increased precision and accuracy, compared to the crisp representations. In 2019 our focus has been on the development of segmentation methods which result in coverage segmentation. We have published (in Journal of Electronic Imaging, Vol 28) a coverage segmentation method based on energy minimization, which improves and generalizes our previously published results. The improved method is applicable to blurred and noisy images, and provides coverage segmentation at increased spatial resolution, while preserving thin fuzzy object boundaries. We have suggested a suitable global optimization scheme to address the challenging non-convex optimization problem. We have evaluated the method on synthetic and real images, confirming its very good performance. Both Buda and Slobodan have defended their PhD theses in 2019, in February and September, respectively.
29. Regional Orthogonal Moments for Texture Analysis Ida-Maria Sintorn
Partner: Vironova AB; Sven Nelander, Dept. of Immunology, Genetics and Pathology, UU Funding: Swedish Research Council
Period:
201501—-Abstract: The purpose of this project is to investigate and systematically characterize a novel approach for texture analysis, which we have termed Regional Orthogonal Moments (ROMs). The idea is to com-bine the descriptive strength and compact information representation of orthogonal moments with the well-established local filtering approach for texture analysis. We will explore ROMs and quantitative texture descriptors derived from the ROM filter responses, and characterize them with special consideration to noise, rotation, contrast, scale robustness, and generalization performance, important factors in applications with natural images. In order to do this we will utilize and expand available image texture datasets and adapt machine learning methods for microscopy image prerequisites. The two main applications for which we will validate the ROM texture analysis framework are viral pathogen detection and identification in MiniTEM images, and glioblastoma phenotyping of patient specific cancer stem cell cultures for disease modeling and personalized treatment. During 2016, a paper comparing and evaluating several ROM filter banks on a number of different texture datasets was submitted and is awaiting the review response.
30. Precise Image-Based Measurements through Irregular Sampling Teo Asplund, Robin Strand, Gunilla Borgefors
Partner: Cris L. Luengo Hendriks-Flagship Biosciences Inc., Westminster, Colorado, USA, Matthew J.
Thurley-Lule˚a University of Technology, Sweden Funding: Swedish Research Council
Period: 20150401–
Abstract: We develop mathematical morphology on irregularly sampled signals. This is beneficial for a number of reasons: 1. Irregularly sampled signals would traditionally have to be resampled onto the regular grid to allow morphology to be applied. However, such resampling can require interpolating data where the original signal contained large holes. This can lead to very poor performance. 2. The morphological operators depend on suprema/infima in the signal. A regularly sampled signal is likely to miss these. 3.
The operators produce lines along which the derivative is not continuous, thereby introducing unbounded frequencies and breaking the correspondence between the sampled signal and the continuous bandlimited one. 4. The structuring element is limited by the sampling grid. We have shown that moving to morphology on irregularly sampled signals can yield results that better approximate continuous morphology, on regularly sampled signals, than the traditional morphological operators, yielding more accurate measurements both in 1D- and 2D grayscale morphology. The framework has also been generalized to allow for adaptive morphology. We have applied the developed methods to irregularly sampled data, such as 3D point clouds, recently in order to segment point clouds of urban scenes. In December of 2019, a PhD-thesis connected to this project was completed. See Figure 28.
Figure 28: Precise Image-Based Measurements through Irregular Sampling
31. Distance Measures Between Images Based on Spatial and Intensity Information, with Applications in Biomedical Image Processing
Johan ¨Ofverstedt, Nataˇsa Sladoje, Joakim Lindblad Partner: Ida-Maria Sintorn, Vironova AB
Funding: VINNOVA, TN-faculty Period: 20170101–
Abstract: Many fundamental image analysis tasks such as image registration, template matching, and im-age retrieval, can be solved successfully by methods utilizing notions of distance (or similarity) between images. Within this project, we study distances combining intensity and efficiently encoded spatial infor-mation, methods for computing them efficiently, and suitable applications where they can lead to robust and accurate solutions. Currently the focus of the project is to develop deformable image registration methods based on these distances, and to develop robust general purpose multi-modal image registration methods.
Recent outcomes include the article ”Fast and Robust Symmetric Image Registration Based on Distances Combining Intensity and Spatial Information” in IEEE TIP, 2019, and the conference publication ”Stochas-tic Distance Transform” orally presented at DGCI, 2019. Two non-reviewed papers, ”Robust Symmetric Affine Image Registration”, and ”Stochastic Distance Functions with Applications in Object Detection and Image Segmentation”, were orally presented at SSBA2019, in G¨oteborg. See Figure 29.
Figure 29: Distance Measures Between Images Based on Spatial and Intensity Information, with
Appli-cations in Biomedical Image Processing
32. Robust learning of geometric equivariances
Karl Bengtsson Bernander, Nataˇsa Sladoje, Joakim Lindblad
Funding: WASP (Wallenberg AI, Autonomous Systems and Software Program) Period: 20180903–
Abstract: The proposed project builds on, and extends work on Geometric deep learning and aims at combining it with Manifold learning, to produce truly learned equivariances without the need for engineered solutions and maximize benefits of shared weights. A decrease of the number of parameters to learn leads to increased performance, generalizability and robustness of the network. An additional gain is in reducing a risk that the augmented data incorporates artefacts not present it the original data. A typical example is textured data, where interpolation performed in augmentation by rotation and scaling unavoidably affects the original texture and may lead to non-reliable results. Reliable texture-based classification is, in many cases, of high importance in biomedical applications. This project is conducted within AI-Math track of WASP the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program, a Swedish national initiative for strategically motivated basic research, education and faculty recruitment. In 2019 we extended the literature study and worked on reproducing the existing methods. We presented a poster at the 4th WASP winter conference in Link¨oping, at the Max Planck Institutes for Intelligent Systems in Stuttgart and T¨ubingen, and at the universities of Darmstadt and Aachen as part of the WASP-AI study trip. See Figure 30.
Figure 30: Robust learning of geometric equivariances
33. Efficient isosurface rendering for visualizationFredrik Nysj¨o, Filip Malmberg, Ingela Nystr¨om Funding: TN faculty
Period: 20180101–
Abstract: Real-time rendering of isosurfaces in large volume datasets can be a challenge, especially for virtual reality applications that require low latency and high update rates. In this project, we develop an efficient hybrid rendering method, RayCaching, that combines rasterisation and raycasting to amortise the cost of rendering a volume over several frames. This work was published in Computer Graphics Forum in 2019. We further develop a memory efficient data structure that allows both rasterisation and ray tracing of isosurfaces extracted from large volume data. This work is now also submitted for publication. See Figure 31.
34. Max-norm optimization in image analysis and computer vision Filip Malmberg, Robin Strand
Partner: Krzysztof C. Ciesielski, Dept. of Mathematics, West Virginia University, Morgantown, WV, USA;
Dept. of Radiology, MIPG, University of Pennsylvania, PA, USA;
Funding: TN faculty Period: 20190101–
Abstract: Many fundamental problems in image processing and computer vision, such as image filtering, segmentation, registration, and stereo vision, can naturally be formulated as optimization problems. Solving
Figure 31: Efficient isosurface rendering for visualization
these optimization problems is often difficult, and generally involves minimizing a non-convex function depending on thousands of variables. Combinatorial, discrete optimization techniques have proven to be very successful in solving optimization problems in many image processing applications. The aim of this project is to study a specific class of optimization problems, where the objective function is defined as the max-norm, or L1-norm, over a set of variables. Such optimization problems have occurred frequently in the image processing literature. It is well known that for many specific max-norm optimization problems, globally optimal solutions can be found using very efficient quasi-linear time algorithms. Notably, the ubiquitous watershed segmentation method can be shown to produce a globally optimal solution to a max-norm optimization problem. Despite the success of these methods in solving certain special cases, their limits in terms of general max-norm optimization remains unclear. The overall aim of this project is to provide a detailed characterization of the class of max-norm problems that can be solved using efficient, low-order polynomial time algorithms. See Figure 32.
Figure 32: Max-norm optimization in image analysis and computer vision
35. Graph neural networks and their application in imagingTeo Asplund, Eva Breznik Funding: department Period: 201909–
Abstract: We investigate graph neural networks for image segmentation, where the aim is to evaluate the role and effectiveness of nonlinearities at various stages. We intend to start with a simplified formulation of a graph convolutional neural network from Wu et. al.: Simplifying Graph Convolutional Networks, which only contains one nonlinearity layer. The simplified network can then be gradually extended with additional nonlinearities of various types. Among them, potentially interesting ones would be operations inspired by mathematical morphology, since they are related to the commonly used max/min filters and could prove beneficial for image data. See Figure 33.