Fig 1.
The basis functions, Uj, k, for performing convolutions are constructed from Fourier modes on concentric circles.
The parameter j determines the radial distance from the centre of the object, while k is the wavenumber. The images show the real and imaginary part of the basis function.
Fig 2.
Comparing the performance of automated and manual counters.
(A) Root mean square error of counts. The correct count for each image is assumed to be the third and final count. Average per image error is shown for the algorithm (blue line) as a function of the number of training samples from the 2012 survey that were used. For comparison, per image error is shown for each of the first pass human counts (red, green lines). (B) Total wildebeest counted within the image set. The final count is shown by the dashed line. The algorithm (blue line) outperforms both human counters in attaining a closer estimate to the true value. This is because the algorithm exhibits no systematic tendency to over or under count. It should be noted that 3000 was the maximum number of training samples available, and it is plausible that the automated total count will drop below the true count before it asymptotes. (C) Individual image errors. The black line is the y = x line for reference. While average per image errors are comparable between automated and human counters, the algorithm makes large errors in a small subset of images. Images that contain many false negatives tend to be darker than the training samples, while false positives occur when there is a lot of structure in the landscape. (D) A comparison of image light levels and under counting. A linear regression shows a significant negative relationship between image light level (average of value component of HSV image) and the amount of under counting (β1 = −1.37, R2 = 0.12). The under count fraction is calculated as and images for which algorithm count > true count are excluded. Point sizes are proportional to the absolute value of the under count of wildebeest in the image.
Table 1.
Comparison of counts between manual and automated methods.
Table 2.
As the accuracy based on the total count does not indicate precision or recall, performance metrics were recorded for a random subset of 100 images. Negative totals are based on the number of non-overlapping regions within each image that are approximately equal in area to a single wildebeest. From these results: precision , recall
.
Fig 3.
From top: Correctly detected wildebeest; Pattern and structure in the landscape frequently lead to false positives; The method is able to distinguish between different species; Species such as zebra, that have distinct body shapes are frequently not identified as wildebeest; The ability to distinguish between species is dependent on sufficient training examples, here the algorithm has misidentified a flock of juvenile ostrich as wildebeest.