A surface specific-line tracking and slope recognition algorithm
Computer Vision, Graphics, and Image Processing
Pattern Recognition Letters
Computer techniques in neuroanatomy
Computer techniques in neuroanatomy
Two-plus-one-dimensional differential geometry
VIP '94 The international conference on volume image processing on Volume image processing
Evaluation of Ridge Seeking Operators for Multimodality Medical Image Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Unbiased Detector of Curvilinear Structures
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Digital Image Processing
CVRMed-MRCAS '97 Proceedings of the First Joint Conference on Computer Vision, Virtual Reality and Robotics in Medicine and Medial Robotics and Computer-Assisted Surgery
Quantitation of Vessel Morphology from 3D MRA
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
CVRMed-MRCAS '97 Proceedings of the First Joint Conference on Computer Vision, Virtual Reality and Robotics in Medicine and Medial Robotics and Computer-Assisted Surgery
Edge Detection and Ridge Detection with Automatic Scale Selection
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Multiscale detection of curvilinear structures in 2-D and 3-D image data
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Ridges for Image Analysis
Extraction of Curved Lines from Images
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
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We introduce a 3D tracing method based on differential geometry in Gaussian blurred images. The line point detection part of the tracing method starts with calculation of the line direction from the eigenvectors of the Hessian matrix. The sub-voxel center line position is estimated from a second order Taylor approximation of the 2D intensity profile perpendicular to the line. In curved line structures the method turns out to be biased. We model the bias in center line position using the first order Taylor expansion of the gradient in scale and position. Based on this model we found that the bias in a torus with a generalized line profile was proportional to σ2. This result was applied in a procedure to remove the bias and to measure the radius of curvature in a curved line structure. The line diameter is obtained using the theoretical scale dependencies of the 0-th and 2nd order Gaussian derivatives at the line center. Experiments on synthetic images reveal that the localization of the centerline is mainly affected by line curvature and is well predicted by our theoretical analysis. The diameter measurement is accurate for diameters as low as 4 voxels. Results in images from a confocal microscope show that the tracing method is able to trace in images highly corrupted with noise and clutter. The diameter measurement procedure turns out to be accurate and largely independent of the scale of observation.