The bispectrum as a source of phase-sensitive invariants for Fourier descriptors: a group-theoretic approach

This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on using the bispectrum in vision show good results when the bispectrum is applied to spherical harmonic models of three-dimensional (3-D) shapes, in particular by improving discrimination over previously-proposed magnitude invariants, and also by allowing detection of neutral pose in human activity detection. The bispectrum has also been formulated for vector spherical harmonics, which have been used in medical imaging for 3-D anatomical modeling. In a paper published in this journal, Smach {\it et al.} use duality theory to establish the completeness of second-order invariants which, as shown here, are the same as the bispectrum. This paper unifies earlier works of various researchers by deriving the bispectrum formula for all compact groups. It also provides a constructive algorithm for recovering functions from their bispectral values on SO(3). The main theoretical result shows that the bispectrum serves as a complete source of invariants for homogeneous spaces of compact groups, including such important domains as the sphere $S^2$

Stitching algorithms for biological specimen images

Abstract: In this paper, we address the problem of combining multiple overlapping image sections of biological specimens to obtain a single image containing the entire specimen. This is useful in the digitisation of a large number of biological specimens stored in museum collections and laboratories. In the case of many large specimens, it means that the specimen must be captured in overlapping sections instead of a single image. In this research, we have compared the performance of several known algorithms for this problem. In addition, we have developed several new algorithms based on matching the geometry (width, slope, and curvature) of the specimens at the boundaries. Finally, we compare the performance of a bagging approach that combines the results from multiple stitching algorithms. Our detailed evaluation shows that brightness-based and curvature-based approaches produce the best matches for the images in this domain

What is hidden in the darkness? Deep-learning assisted large-scale protein family curation uncovers novel protein families and folds

Driven by the development and upscaling of fast genome sequencing and assembly pipelines, the number of protein-coding sequences deposited in public protein sequence databases is increasing exponentially. Recently, the dramatic success of deep learning-based approaches applied to protein structure prediction has done the same for protein structures. We are now entering a new era in protein sequence and structure annotation, with hundreds of millions of predicted protein structures made available through the AlphaFold database. These models cover most of the catalogued natural proteins, including those difficult to annotate for function or putative biological role based on standard, homology-based approaches. In this work, we quantified how much of such "dark matter" of the natural protein universe was structurally illuminated by AlphaFold2 and modelled this diversity as an interactive sequence similarity network that can be navigated at https://uniprot3d.org/atlas/AFDB90v4 . In the process, we discovered multiple novel protein families by searching for novelties from sequence, structure, and semantic perspectives. We added a number of them to Pfam, and experimentally demonstrate that one of these belongs to a novel superfamily of toxin-antitoxin systems, TumE-TumA. This work highlights the role of large-scale, evolution-driven protein comparison efforts in combination with structural similarities, genomic context conservation, and deep-learning based function prediction tools for the identification of novel protein families, aiding not only annotation and classification efforts but also the curation and prioritisation of target proteins for experimental characterisation

Moment Forms Invariant to Rotation and Blur in Arbitrary Number of Dimensions

We present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions. Moment invariants to convolution with an arbitrary centrosymmetric filter are derived first, and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance. Several examples of the invariants are calculated explicitly to illustrate the proposed procedure. Their invariance, robustness, and capability of using in template matching and in image registration are demonstrated on 3D MRI data and 2D indoor images

局所画像モーメントに基づくブラー画像マッチングに関する研究

Tohoku University北村喜文課

Doctor of Philosophy

dissertationInteractive editing and manipulation of digital media is a fundamental component in digital content creation. One media in particular, digital imagery, has seen a recent increase in popularity of its large or even massive image formats. Unfortunately, current systems and techniques are rarely concerned with scalability or usability with these large images. Moreover, processing massive (or even large) imagery is assumed to be an off-line, automatic process, although many problems associated with these datasets require human intervention for high quality results. This dissertation details how to design interactive image techniques that scale. In particular, massive imagery is typically constructed as a seamless mosaic of many smaller images. The focus of this work is the creation of new technologies to enable user interaction in the formation of these large mosaics. While an interactive system for all stages of the mosaic creation pipeline is a long-term research goal, this dissertation concentrates on the last phase of the mosaic creation pipeline - the composition of registered images into a seamless composite. The work detailed in this dissertation provides the technologies to fully realize interactive editing in mosaic composition on image collections ranging from the very small to massive in scale