Estimation of intrinsic volumes from digital grey-scale images
This addresses the issue of accurate geometric measurement from blurred grey-scale images in fields like image analysis and computer vision, representing an incremental improvement over existing black-and-white methods.
The paper tackles the problem of biased estimation of intrinsic volumes from digital images by extending local algorithms to directly process grey-scale images without thresholding, resulting in asymptotically unbiased estimators for surface area and integrated mean curvature as resolution increases.
Local algorithms are common tools for estimating intrinsic volumes from black-and-white digital images. However, these algorithms are typically biased in the design based setting, even when the resolution tends to infinity. Moreover, images recorded in practice are most often blurred grey-scale images rather than black-and-white. In this paper, an extended definition of local algorithms, applying directly to grey-scale images without thresholding, is suggested. We investigate the asymptotics of these new algorithms when the resolution tends to infinity and apply this to construct estimators for surface area and integrated mean curvature that are asymptotically unbiased in certain natural settings.