A novel method of estimating structure model index from gray-level images

According to the standard approach, estimation of the structure model index (SMI) of a trabecular bone sample has to be preceded by segmentation of the bone image and then triangulation of the trabecular surface. However, when analyzing clinical data, image segmentation should be avoided whenever possible, due to difficulties in controlling binarization artifacts. The aim of the present study is to develop a method to estimate SMI directly from gray-level images, without prior segmentation. It is shown that the standard definition of SMI can be formulated in terms of integrals of the gray-level intensity and the magnitude of the gray-level intensity gradient, computed for the analyzed image and the image eroded by an infinitesimal ball structuring element. Because in a real application the size of an eroding element is always finite, a procedure is proposed to reduce the finite size errors. The performance of the proposed method is tested for structures with known SMI. Next, based on a set of μCT images of trabecular bone from the distal radius, the proposed and the standard methods are compared. It is shown that the proposed novel approach is statistically equivalent to the standard one, if applied to high-resolution μCT data. The influence of clinically relevant factors like limited resolution and noise on the estimation of SMI is tested. It is shown that the gray-level approach is more robust against image degradation factors than the standard one.