A model-based inversion method was used to obtain quantitative estimates of histological parameters from multispectral images of the colon and to examine their potential for discriminating between normal and pathological tissues. Pixel-wise estimates of the mucosal blood volume fraction, density of the scattering particles and thickness were derived using a two-stage method. In the first (forward) stage reflectance spectra corresponding to given instances of the parameter values were computed using Monte Carlo simulation of photon propagation through a multi-layered tissue. In the second (inversion) stage the parameter values were obtained via optimization using an iterated conditional modes algorithm based on Discrete Markov Random Fields. The method was validated on computer generated data contaminated with noise giving a mean normalized root mean square deviation (NRMSD) of 2.04. Validation on ex vivo images demonstrated that parametric maps show gross correspondence with histological features of mucosa characteristic of cancerous, precancerous and noncancerous colon lesions. The key signs of abnormality were shown to be the increase in the blood volume fraction and decrease in the density of scattering particles.

One of the common physiological changes associated with cancer is the formation of a dense, irregular and leaky network of new blood vessels, which result in the increase of the blood volume fraction (BVF) at the site of a tumour. Such changes are not always obvious through visual inspection using a direct observation, an endoscopic device or colour photography. This paper presents a method for deriving quantitative estimates of BVF of the colon mucosa from multispectral images of the colon. The method has two stages. In the first ("forward") stage a physics-based model of light propagation computes the spectra corresponding to a range of instances of the colon tissue, and in particular the spectral changes resulting from changes in the quantity of blood volume fraction, haemoglobin saturation, the size and density of scattering particles, and the tissue thickness. In the second stage ("model inversion") the spectra obtained from the image data are used to derive the values of the above histological parameters. Parametric maps of the blood contents are created by storing at every pixel the BVF value recovered through the model inversion. In a pilot study multispectral images of ex-vivo samples of the colon were acquired from 8 patients. The samples contained histologically confirmed instances of adenocarcinoma and other pathologies. The parametric maps of BVF showed the significant increase in blood volume fraction (up to 75% above that of the surrounding the normal tissue). A Mann-Whitney test with Bonferroni correction showed that all but one of the differences (a benign neoplastic polyp) are significant (p < 0.000 15).

This paper describes a novel method for quantitative interpretation of multispectral images. By constructing an optical model of a tissue and by modelling the image formation process we predict the spectral composition of light remitted from the tissue. The parameters characterising the tissue are varied to represent the entire range of tissue instances. The modelling of image formation is used in place of statistical modelling in which training is performed using measured data with known parameterisation. In this way the method overcomes a common problem in medical imaging where “ground truth” data can be impossible to obtain. The paper shows application of the method to the recovery of histological parameters characterising the skin, the eye and the colon.

Theoretical models of the signal detected by a CCD camera during hyperspectral imaging with an integrating sphere are derived using Markov chains with absorbing states. The models provide analytical expressions that describe the real reflectance of the sample as a function of the detected signal at each pixel of the image. Validation of the models was done by using reflectance standards and tissue phantoms. The models provide accurate analytical solutions for samples and spheres that are near-Lambertian reflectors.

Colon cancer alters the tissue macro-architecture. Changes include increase in blood content and distortion of the collagen matrix, which affect the reflectance spectra of the colon and its colouration. We have developed a physics-based model for predicting colon tissue spectra. The colon structure is represented by three layers: mucosa, submucosa and smooth muscle. Each layer is represented by parameters defining its optical properties: molar concentration and absorption coefficients of haemoglobins, describing absorption of light; size and density of collagen fibres; refractive index of the medium and collagen fibres, describing light scattering; and layer thicknesses. Spectra were calculated using the Monte Carlo method. The output of the model was compared to experimental data comprising 50 spectra acquired in vivo from normal tissue. The extracted histological parameters showed good agreement with known values. An experiment was carried out to study the differences between normal and abnormal tissue. These were characterised by increased blood content and decreased collagen density, which is consistent with known differences between normal and abnormal tissue. This suggests that histological quantities of the colon could be computed from its reflectance spectra. The method is likely to have diagnostic value in the early detection of colon cancer.

Two distance measures for attributed graphs are presented that are based on the maximal similarity common subgraph of two graphs. They are generalizations of two existing distance measures based on the maximal common subgraph. The new measures are superior to the well-known measures based on elementary edit transformations in that no particular edit operations (together with their costs) need to be defined. Moreover, they can deal not only with structural distortions, but also with perturbations of attributes. It is shown that the new distance measures are metrics.

We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuous-valued attributes and can be applied to rooted as well as unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomial-time algorithm to compute them. This is a remarkable and attractive property, since the computation of traditional edit-distance-based metrics is, in general, NP-complete, at least in the unordered case. We experimentally validate the usefulness of our metrics on shape matching tasks and compare them with (an approximation of) edit-distance.

We address the problem of comparing attributed trees and propose four novel distance metrics centered around the notion of a maximal similarity common subtree, and hence can be computed in polynomial time. We experimentally validate the usefulness of our metrics on shape matching tasks, and compare them with edit-distance.

We derive a continuous probability distribution which generates neighbours of a point in an interval in a similar way to the bitwise mutation of a Gray code binary string. This distribution has some interesting scale-free properties which are analogues of properties of the Gray code neighbourhood structure. A simple (1+1)-ES using the new distribution is proposed and evaluated on a set of benchmark problems, on which it performs remarkably well. The critical parameter is the precision of the distribution, which corresponds to the string length in the discrete case. The algorithm is also tested on a difficult real-world problem from medical imaging, on which it also performs well. Some observations concerning the scale-free properties of the distribution are made, although further analysis is required to understand why this simple algorithm works so well.

The colour of colon tissue, which depends on the tissue structure, its optical properties, and the quantities of the pigments present in it, can be predicted by a physics-based model of colouration. The model, created by analysing light interaction with the tissue, is aimed at correlating the histology of the colon and its colours. This could be of a great diagnostic value, as the development of tissue abnormalities and malignancies is characterised by the rearrangement of underlying histology. Once developed, the model has to be validated for correctness. The validation has been implemented as an optimisation problem, and evolutionary techniques have been applied to solve it. An adaptive approximate optimisation method has been developed and applied in order to speed up the computationally expensive optimisation process. This works by iteratively improving a surrogate model based on an approximate physical theory of light propagation (Kubelka Munk). Good fittings, obtained under the histologically plausible values of model parameters, are presented. The performances of the new method were compared to that of a simple Evolution Strategy which uses an accurate, but expensive, Monte Carlo method. The new method is general and can be applied with any surrogate model for optimisation.