Math 290J (section 3) current literature in applied mathematics
Mathematical models for image processing and medical imaging
(joint with the activity group SIG-PDE from the Center for Computational Biology)
Organizer: Luminita Vese. E-mail: firstname.lastname@example.org
Presentations, Time and Location:
Thursday, October 25, time 12pm, location BH 3811: Presentation by JPL (Igor Yanovsky and colleagues) jointly with the Vision Lab (optional)
Thursday, October 2, time 2pm, location MS 6627: Speaker John Wright, visiting PhD student, University of Illinois at Urbana-Champaign
Title: Dense Error Correction via $L^1$-Minimization
Wednesday, October 15, time 3-4pm, MS 5203: Speaker Yunho Kim (UCLA).
Title: Image Recovery Using Functions of Bounded Variation and Sobolev Spaces of Negative Differentiability
Friday, October 17, time 2-3pm, MS 6221: guest lecturer Leah-Bar, University of Minnesota, Electrical and Computer Engineering Dept.
Title: Variational Image Restoration with Segmentation-based Regularization
Wednesday, October 29, time 4-5pm, MS 6229: Facundo Memoli (Stanford University): $L^p$ Gromov Hausdorff Distances for Shape-Matching
Friday November 07, 2008, time 2-3pm, MS 6627: guest lecturer Emmanuel Candes (Caltech), Exact matrix completion via convex optimization
Monday, November 17: Yunho Kim, UCLA (continuation), in MS 7629
Monday, Nov. 24: Juan Eugenio Iglesias (UCLA), MS 7629.
Semiautomatic Segmentation of Vertebrae in Lateral X-rays Using a
Conditional Shape Model
Rationale and Objectives
Manual annotation of the full contour of the vertebrae in lateral x-rays for subsequent
morphometry is time-consuming. The standard six-point morphometry is commonly used instead.
It has been shown that the information from the complete contour improves the quality of the
study. In this article, the six landmarks are given and the vertebrae are segmented taking
advantage of that information. The result is a semiautomatic system in which the full contour
is found with high precision, and that only requires a radiologist to mark six points per
Materials and Methods
A shape model was built for both the six landmarks and the full contours of the vertebrae L1,
L2, L3, and L4 of 142 patients. The distribution of the principal components of the full
contour was then modeled as a Gaussian conditional distribution depending on the principal
components of the six landmarks. The conditional mean was used as initialization for active
shape model optimization, and the conditional variance was used to constrain the solution to
The achieved point-to-line error was 0.48 mm, and 95% of the points were located within 1.36
mm of the annotated contour. The accuracy is superior to those of previously published
studies, at the expense of requiring the six points to be marked. Fractures and osteophytes
are well approximated by the model, although they are sometimes oversmoothed.
The proposed method provides hence a richer description than the six points, and can be used
as input for shape-based morphometry to detect and quantify vertebral deformation more
Monday, Dec. 1st: time 2-3pm, MS 7629
Monday, Dec. 08
Participants: Pascal Getreuer, Juan Eugenio Iglesias Gonzalez, Jahanshad Neda, Yunho Kim, Mi Youn Jung, Tungyou Lin, Mark Roden, Carl Lederman, Yingying Li.