M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Robust similarity registration technique for volumetric shapes represented by characteristic functions

This paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by their characteristic functions (CFs). Here, the calculation of rotation parameters is considered as a spherical crosscorrelation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis (PCA).Thus, fast Fourier transform (FFT) is employed to vastly improve efficiency and robustness. Geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters. It is numericallydemonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses. Further validation of our method is performed by registering a lung database

Fundamental remote sensing science research program. Part 1: Status report of the mathematical pattern recognition and image analysis project

The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of the Earth from remotely sensed measurement of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inference about the Earth

Frequency characteristics of aerial scenes with respect to a video imagining system

Thesis (M.A.)--Boston UniversityAn overall investigation is made of operating characteristics, theoretical limitations and optimum range values for video communication of aerial scenes. Reasons are given for the selection of a particular receiver and the importance of this type of study is indicated from the A.D.P. crystals' complex A.C. frequency response. The restricted contrast range, due to haze, is noted in evaluating the various video systems

Design synthesis and shape generation

If we are to capitalise on the potential that a design approach might bring to innovation in business and society, we need to build a better understanding of the evolving skill-sets that designers will need and the contexts within which design might operate. This demands more discourse between those involved in cutting edge practice, the researchers who help to uncover principles, codify knowledge and create theories and the educators who are nurturing future design talent. This book promotes such a discourse by reporting on the work of twenty research teams who explored different facets of future design activity as part of Phase 2 of the UK's research council supported Designing for the 21st Century Research Initiative. Each of these contributions describes the origins of the project, the research team and their project aims, the research methods used and the new knowledge and understanding generated. Editor and Initiative Director, Professor Tom Inns, provides an introductory chapter that suggests ways the reader might navigate these viewpoints. This chapter concludes with an overview of the key lessons that might be learnt from this collection of design research activity