Grey-Scale Measurements in Multi-Dimensional Digitized Images

摘要

In this thesis we propose new methods for estimating properties of analog objectsin properly sampled multi-dimensional grey-scale images. We focus only on point measurements and object measurements. The theory for most measurements holds irrespective of the image dimension. For practical purposes, we have emphasized properties related to 2D and 3D images. Chapter 1 introduces the field of image analysis. In Chapter 2, attention is paid to image formation using an 'ideal' optical system. As an example we have chosen a microscope, an optical instrument for which diffraction limited optics are widely available. Chapter 3 deals with the systematic errors of second derivative operators applied to low-pass filtered curved edges. In chapter 4 combinations-of-Gaussians for edge localization are studied. Chapter 5 explains curvature estimation of isophotes. Chapter 6 introduces object measurements by estimating 2D area and 3D volume. Chapter 7 presents a method for the estimation of 2D edge length (contour length) and 3D surface area. Chapter 8 gives a short description of 3D length estimators. In Chapter 9 we discuss a shape descriptor: bending energy.