Estimating statistics in arbitrary regions of interest

We address the problem of estimating statistics in regions of interest (ROIs) containing both whole and partial pixels. Such ROIs arise frequently in vision problems such as segmentation and registration. For example, even where the control points of an ROI, say the vertices of a polygon, are forcibly aligned with the pixel grid, the connecting edges will rarely do so. In medical image analysis, for instance, this can be a cause of significant error. More generally, any cost function that includes statistics estimated from the image will often exhibit irregularities due to such partial pixels. Our proposed solution addresses this problem by correctly accounting for the partial pixel area. Moreover, the method has no arbitrary parameters such as bin widths or kernel sizes. It implicitly addresses the issue of independence and gives rise to continuous density estimates whose quality is, in principle at least, independent of the number of pixels in the ROI. We present results to compare our proposed method with conventional techniques such as weighted histograms and Parzen windowing.