Cse 252c: Computer Vision Iii Distributions and Histograms-of-x 3.1. Histograms

Used fairly frequently in computer vision in the late 1990s, histograms are a convenient way of packaging a distribution. A histogram (Fig. 1) is a non-parametric estimate of a density, in contrast to a parametric approach such as fitting a Gaussian to a sample of data, which is completely defined by two parameters. Histograms, on the other hand, are defined by their bin sizes. Similar to choosing k or σ, bin size selection is a hard problem. A related idea is the kernel density estimate, which puts a kernel (e.g . a Gaussian) around each data point. Instead of binning, we must choose an appropriate kernel width. Such model selection problems are often solved in practice using cross validation and/or information theoretic methods. In a nutshell, histograms are relevant to object recognition in that they allow us to do recognition without feature correspondence (Schiele and Crowley, 2000). At first glance, this seems surprising, since histograms (viz. global