We propose a method for identifying a set of colours for displaying 2-D and 3-D categorical images when the categories are unordered labels. The principle is to find maximally distinct sets of colours. We either generate colours sequentially, to maximise the dissimilarity or distance between a new colour and the set of colours already chosen, or use a simulated annealing algorithm to find a set of colours of specified size. In both cases, we use a Euclidean metric on the perceptual colour space, CIE-LAB, to specify distances.
Image analysis methods for estimating size of object features extract pixel-based measurements, after object segmentation, then convert these to an estimate of actual size; e.g. segmentation of a cell in a randomly located 2-D cross-sectional image, counting no. of pixels on the cell boundary, and converting to an estimate of cell surface area using geometrical formulae. Stereology takes a quite different approach to estimating higher dimensional properties of an object, by using a randomly orientated 2-D specimen section or 2-D projection of a 3-D object. Geometrical properties and sampling theory enable inference of 3-D properties; e.g. feature length is estimated by counting intersections with a randomly superimposed test grid with fixed known spacing. This work compares these two approaches for image feature length estimation, using a simulation study. We generate binary straight line structures and planar curves of known size and compare results from several different estimators of feature length, including a novel estimator which weights pixel count by estimating local curve orientation.
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