GIPHOD ver. 2.0 is a program realized to show how we can selectively remove the natural invariance of persistent homology with respect to every homeomorphism and preserve only the invariance chosen by the user. This property is important for applications in computer vision and pattern recognition.

GIPHOD uses a dataset of 10000 quite simple synthetic gray-scale images, represented as functions from the square [0,1]x[0,1] to the interval [0,1] (1=white, 0=black). 1000 images (call this set X) are randomly generated, whereas the remaining 9000 images are obtained by applying transformations composed of translations, rotations and reflections to the images in the set X (let us call this set Y).

Differently from GIPHOD ver. 1.0, GIPHOD ver. 2.0 does not ask the user to choose an invariance group. Instead, two windows are available. The user is only requested to choose at least two positive examples in the top window, and at least two negative examples in the bottom window. Positive examples are pictures that are considered by the user quite similar to the picture Q he/she is looking for, while negative examples are pictures that are considered by the user quite different from Q. GIPHOD looks for the ten most similar images in our dataset (consisting of the sets X and Y) by taking into account the positive and negative examples that have been chosen. Among these ten images, the ones that are judged to respect the user's choices are displayed in green. You can browse the images in our dataset Y here.

If you are interested in details about the algorithms behind GIPHOD, you can find them here.

Please send us your suggestions to improve GIPHOD.

Go Back Main page