On Achievable Accuracy in Edge Localization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Cramer-Rao lower bounds for estimation of a circular arc center and its radius
Graphical Models and Image Processing
On the Precision in Estimating the Location of Edges and Corners
Journal of Mathematical Imaging and Vision
Cramer-Rao lower bounds for curve fitting
Graphical Models and Image Processing
Journal of Mathematical Imaging and Vision
Limits on estimating the width of thin tubular structures in 3d images
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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This work analyses the accuracy of estimating the location of 3D landmarks and characteristic image structures. Based on nonlinear estimation theory we study the minimal stochastic errors of the position estimate caused by noisy data. Given analytic models of the image intensities we derive closed-form expressions for the Cramér-Rao bound for different 3D structures such as 3D edges, 3D ridges, 3D lines, and 3D blobs. It turns out, that the precision of localization depends on the noise level, the size of the region-of-interest, the width of the intensity transitions, as well as on other parameters describing the considered image structure. The derived lower bounds can serve as benchmarks and the performance of existing algorithms can be compared with them. To give an impression of the achievable accuracy numeric examples are presented. Moreover, by experimental investigations we demonstrate that the derived lower bounds can be achieved by fitting parametric intensity models directly to the image data.