mfeurer
commented
6 years ago Original publication: http://www.dmi.usherb.ca/~larocheh/publications/deep-nets-icml-07.pdf
3.3. Recognition of Convex Sets: The task of discriminating between tall and wide rectangles was designed to exhibit the learning algorithms’ ability to process certain image shapes and learn their properties. Following the same principle, we designed another learning problem which consists in indicating if a set of pixels forms a convex set. Like the MNIST dataset, the convex and non-convex datasets both consist of images of 28 × 28 pixels. The convex sets consist of a single convex region with pixels of value 255 (white). Candidate convex images were constructed by taking the intersection of a random number of half-planes whose location and orientation were chosen uniformly at random. Candidate non-convex images were constructed by taking the union of a random number of convex sets generated as above. 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 in the set is the same. The generated training, validation and test sets are of size 6000, 2000 and 50000 respectively. Samples for this tasks are displayed in figure 6.
I just tagged these datasets as origin unknown: https://www.openml.org/d/40765 https://www.openml.org/d/40766
If we were to obtain the publication, we might be able to use it