The surface model of the tiger, stored as a text file of three-dimensional coordinates, extends from the shoulders to the base of the tail, undercutting the fore and hind limbs. shows the model fit to a camera trap image and the pattern sample scanned from the flank region. The surface model vertices are the endpoints of rays emanating at intervals from an internal spine, the ray lengths at each interval forming a cosine series function of angle from the dorsal midline, so that initially the model is bilaterally symmetrical. The series coefficients are fixed and were determined by least squares fit to a cloud of surface points generated by photogrammetry, using photographs of a zoo tiger. The computer program initially scales, translates and rotates the model by minimizing the sum of squared distances from shoulder, hip and tail base points on the model to corresponding points on the image, positioned manually on the screen by the user. The model can also twist and bend and thicken or thin differentially along its long axis. A set of four bi-quadratic splines determine the bending and twisting angles and the expansion factors along the model spine. The spline node coordinates introduce a further set of parameters that are then used in conjunction with the scale, translation and rotation parameters to optimize the fit of the projected model to image margins marked by the user.
Figure 1 The three-dimensional model fitted to a camera trap image of a tiger. The yellow dots placed on the screen by the user indicate the position of shoulder, hip and tail base points and the red and blue dots indicate the upper and lower margins of the image, (more ...)
The same procedure is used to scan left and right flank pattern samples from a photograph of a skin laid flat, except that the surface model used is planar and is not permitted to bend or twist. Thus, as for the live animal photographs, the pattern samples are largely unaffected by camera angle or the scale and orientation of the image.
The pattern sample scanned via the model from the new image is then compared with the database of previous samples. Two algorithms are used to calculate a similarity score between each pair of pattern samples. We omit the details here because a variety of algorithms are available for comparing patterns, but note that, by combining algorithms that are to some extent complementary, it is possible to reduce the risk of obtaining a low score between matching patterns (i.e. those scanned from images of the same tiger). One of the algorithms is robust to noise in the image but fails when regions of the image are occluded, and the other is robust to occluded regions but sensitive to noise.
The final similarity score is calculated as the posterior probability that the patterns are from images of the same tiger, given the values returned by the two algorithms. The prior probability that two randomly chosen images are of the same tiger could be adjusted to reflect the recorded sex, age and location of the images, but in this case is set simply to the reciprocal of an assumed, local population size, N
. If Sc
are the values returned by the two algorithms, the posterior probability that the patterns are from images of the same tiger is given by
|non-match|) and P
|match) are the joint densities of Sc
for non-matching and matching pattern pairs, and are estimated from the frequency distributions of the scores that each member of the pair accumulated as it was compared with the existing catalogue. The value of N
affects the posterior probability but not the rank order of the existing individuals. In addition to combining the values into a single similarity score, the posterior probability reduces the expected rank of individuals that tend to achieve higher than average algorithm values (those represented only by low-quality images).
The posterior match probability can be compared with a threshold value, so that only those catalogue individuals from which at least one pattern sample exceeds the threshold are checked visually against the new images. However, in the tiger system, all catalogue animals are ranked in order of decreasing maximum posterior probability, so that the user has the option to search the entire catalogue and any existing match will be found as soon as possible.