Learning to hash logistic regression for fast 3D scan point classification

Segmenting range data into semantic categories has become a more and more active field of research in robotics. In this paper, we advocate to view this task as a problem of fast, large-scale retrieval. Intuitively, given a dataset of millions of labeled scan points and their neighborhoods, we simply search for similar points in the datasets and use the labels of the retrieved ones to predict the labels of a novel point using some local prediction model such as majority vote or logistic regression. However, actually carrying this out requires highly efficient ways of (1) storing millions of scan points in memory and (2) quickly finding similar scan points to a target scan point. In this paper, we propose to address both issues by employing Weiss et al.'s recent spectral hashing. It represents each item in a database by a compact binary code that is constructed so that similar items will have similar binary code words. In turn, similar neighbors have codes within a small Hamming distance of the code for the query. Then, we learn a logistic regression model locally over all points with the same binary code word. Our experiments on real world 3D scans show that the resulting approach, called spectrally hashed logistic regression, can be ultra fast at prediction time and outperforms state-of-the art approaches such as logistic regression and nearest neighbor.