Fast Invariant Feature Extraction for Image Retrieval

Invariant features remain unchanged when the data is transformed according to a group action. This property can be useful for applications in which a geometric transformation like a change in an object’s position and orientation is irrelevant and one is only interested in the object’s intrinsic features. We discuss features for the group of Euclidean motion (both for gray-valued or multichannel 2D and 3D data) that are calculated by an integration over the transformation group (Haar integrals). However, their computation time, even though it is of linear complexity, is too high for applications that either require a fast response (e.g. image retrieval) or have big data set sizes (e.g. 3D tomographic data). The original idea described here is to estimate the features via a Monte-Carlo method instead of carrying out a deterministic computation, thus obtaining complexity 0(1). For a typical 3D application this results in speedup factors of 105–106. Error bounds for the method are theoretically derived and experimentally verified. Beside the reduction in computation time, the method is less sensitive to numerical errors which can be a problem of the deterministic calculation especially for large data sets. An image retrieval application demonstrates the potential of the presented features.