In this section, a prior model is given for the location, scale, orientation and shape of a fish. A fish is treated as a 2D object summarized by k=25 landmarks along its outline. An alternative approach is to model the fish outlines with a composite of geometric shapes (ellipses, parabolas and triangles) [ 11 ] but it was found that the landmark-based approach modelled the fish outlines more closely.
To describe variability in shape a Point Distribution Model [ 3 ] was constructed based on a training sample of 20 fish images. After centring and scaling the outlines so that the centre of gravity is at the origin and the sum of squared landmark coodinates equals unity, a Procrustes analysis [ 9 ] gives the template fish shape, which for convenience can be rotated to be horizontally aligned. A principal component analysis performed in the tangent space to shape space gives the modes of shape variability to deform the template. These modes of variation provide a summary both of the variation between individuals and the deformations in shape caused by swimming. We found that the first 5 components accounted for 70% of the variation; the first 10 components accounted for 90%. In this work, the first 10 principal components have been retained to represent the shape variability. The average shape and a few principal components are illustrated in Fig. 1 .
Each object is thus modelled by a set of variables
which includes the 5
pose
variables, location
, scale
s
, orientation
, and reflection
,
and 10
shape
variables (which describe the deviations from the template in the
principal component directions). The prior distribution of these
variables was obtained by inspection of the training sample and is
specified in terms of the following independent random variables: the
location variables are given a uniform distribution over the image, the
scale
s
(in pixels) and the orientation
(in degrees) are given normal distributions (truncated at
) with respect to the template:
and reflection was treated as a discrete variable sampled from two states with equal probability. The principal components were given normal distributions with the same variability observed in the training data. For visualization, it is useful to note that when s takes its average value, 187, the template fish has a length of 115 pixels in the image.
K De Souza