Proposed BSc/MSc Project for AY 2005-2006

Radon transform based super-resolution algorithm for

shape reconstruction

Keywords: Radon transforms, Tomographic reconstructions, Geometric moments, Sampling of signals with Finite Rate of Innovation (FRI), and Annihilating filter methods.

Required skills: Basic knowledge of DSP, interest (and aptitude) towards GUI development in Matlab (or C++ or Java).

Number of students: One.

Secondary support: Mr Pancham Shukla (RA and PhD student of Dr P L Dragotti)

Room 808, http://www.commsp.ee.ic.ac.uk/~pancham/index.html

Abstract: In many applications such as determination of crop yield, illegal intrusion in vast land fields, military and defence surveillance, geophysical explorations, and robot vision, it is important to determine 2-D (or 3-D) objects (or their coordinates) with high precision from blurred and sampled images (digital images) obtained trough CCD cameras or radiation sensors (optical or microwave scanners). In many situations, the actual imagery can be modelled by a set of shapes with Finite Rate of Innovation (FRI) (e.g. polygons, circles, and ellipses). Super-resolution shape reconstruction deals with precise determination of such shapes from their blurred version(s).

It is interesting to know that shapes and dimensions of unknown 2-D (or 3-D) objects can be determined (reconstructed) by taking Radon transform projections at finite number of viewing angles (within [0,180) degrees) and then projecting them back on the same plane. The famous example of this technique is tomographic reconstruction (CT scanning) of human body. Furthermore, the Radon transform projections of an object are also linked with the object’s geometric moments. Using this link, one can take moments of the projections of the (blurred and sampled version of the) given FRI object at various angles, and then by using sophisticated back projection algorithms (e.g. annihilation filter for moments), one can determine the coordinates of the object with infinite precision.

In this project, student will gain the understanding of recently developed sampling theories (FRI sampling), fundamental aspects of tomographic reconstruction used in modern medical scanners, connection between moments and Radon projections, and its signal/image processing applications in determining image shapes. Student will start with estimation of simple shapes such as polygons and thereafter polygons containing polygonal holes, and other smooth objects with unknown boundaries. Finally, the student is expected to develop a professional looking shape reconstruction GUI in Matlab (or C++ or Java) for phantom as well as real images. The student will acquire a privilege of using high-end digital camera of the laboratory for his GUI development.