Recognition of convex sets
The convex sets consist of a single convex region with pixels of value 255. Candidate convex images were constructed by taking the intersection of a number of half-planes whose location and orientation were chosen uniformly at random. The number of intersecting half-planes was also sampled randomly according to a geometric distribution with parameter 0.195. A candidate convex image was rejected if there were less than 19 pixels in the convex region.
Candidate non-convex images were constructed by taking the union of a random number of convex sets generated as above, but with the number of half-planes sampled from a geometric distribution with parameter 0.07 and with a minimum number of 10
pixels. The number of convex sets was sampled uniformly from 2 to 4. The candidate non-convex images were then tested by checking a convexity condition for every pair of pixels in the non-convex set. Those sets that failed the convexity test were added to the dataset.
The parameters for generating the convex and non-convex sets were balanced to ensure that the mean number of pixels of value 255 is the same in the two datasets.
All the datasets are provided as zip archives. Each archive contains two files -- a training (and validation) set and a test set. We used the last 2000 examples of the training sets as validation sets and, in the case of SVMs, retrained the models with the entire set after choosing the optimal parameters on these validation sets. Data is stored at one example per row, the features being space-separated. There are 784 features per example (=28*28 images), corresponding to the first 784 columns of each row. The last column is the label, which is 1 or 0 .
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if you are interested in the (MATLAB) scripts that we used to generate this data.
- 21 Jun 2007