We define a "good image cluster" as one in which images can be easily composed (like a puzzle) using pieces from each other, while are difficult to compose from images outside the cluster. The larger and more statistically significant the pieces are, the stronger the affinity between the images. This gives rise to unsupervised discovery of very challenging image categories. We further show how multiple images can be composed from each other simultaneously and efficiently using a collaborative randomized search algorithm. This collaborative process exploits the "wisdom of crowds of images", to obtain a sparse yet meaningful set of image affinities, and in time which is almost linear in the size of the image collection. "Clustering-by-Composition" yields state-of-the-art results on current benchmark data sets. It further yields promising results on new challenging data sets, such as data sets with very few images (where a `cluster model' cannot be `learned' by current methods), and a subset of the PASCAL VOC data set (with huge variability in scale and appearance).

Given a set of images which share an object from the same semantic category, we would like to co-segment the shared object. We define 'good' co-segments to be ones which can be easily composed (like a puzzle) from large pieces of other co-segments, yet are difficult to compose from remaining image parts. These pieces must not only match well but also be statistically significant (hard to compose at random). This gives rise to co-segmentation of objects in very challenging scenarios with large variations in appearance, shape and large amounts of clutter. We further show how multiple images can collaborate and "score" each others' co-segments to improve the overall fidelity and accuracy of the co-segmentation. Our co-segmentation can be applied both to large image collections, as well as to very few images (where there is too little data for unsupervised learning). At the extreme, it can be applied even to a single image, to extract its co-occurring objects. Our approach obtains state-of-the-art results on benchmark datasets. We further show very encouraging co-segmentation results on the challenging PASCAL-VOC dataset.

Spatial Super Resolution (SR) aims to recover fine image details, smaller than a pixel size. Temporal SR aims to recover rapid dynamic events that occur faster than the video frame-rate, and are therefore invisible or seen incorrectly in the video sequence. Previous methods for Space-Time SR combined information from multiple video recordings of the same dynamic scene. In this paper we show how this can be done from a single video recording. Our approach is based on the observation that small space-time patches (`ST-patches', e.g., 5×5×3) of a single `natural video', recur many times inside the same video sequence at multiple spatio-temporal scales. We statistically explore the degree of these ST-patch recurrences inside `natural videos', and show that this is a very strong statistical phenomenon. Space-time SR is obtained by combining information from multiple ST-patches at sub-frame accuracy. We show how finding similar ST-patches can be done both efficiently (with a randomized-based search in space-time), and at sub-frame accuracy (despite severe motion aliasing). Our approach is particularly useful for temporal SR, resolving both severe motion aliasing and severe motion blur in complex `natural videos'.