A graph-spectral approach to shape-from-shading

In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery

Shape-from-shading using the heat equation

This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces

Laser Based Mid-Infrared Spectroscopic Imaging – Exploring a Novel Method for Application in Cancer Diagnosis

A number of biomedical studies have shown that mid-infrared spectroscopic images can provide both morphological and biochemical information that can be used for the diagnosis of cancer. Whilst this technique has shown great potential it has yet to be employed by the medical profession. By replacing the conventional broadband thermal source employed in modern FTIR spectrometers with high-brightness, broadly tuneable laser based sources (QCLs and OPGs) we aim to solve one of the main obstacles to the transfer of this technology to the medical arena; namely poor signal to noise ratios at high spatial resolutions and short image acquisition times. In this thesis we take the first steps towards developing the optimum experimental configuration, the data processing algorithms and the spectroscopic image contrast and enhancement methods needed to utilise these high intensity laser based sources. We show that a QCL system is better suited to providing numerical absorbance values (biochemical information) than an OPG system primarily due to the QCL pulse stability. We also discuss practical protocols for the application of spectroscopic imaging to cancer diagnosis and present our spectroscopic imaging results from our laser based spectroscopic imaging experiments of oesophageal cancer tissue