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: lvese@math.ucla.edu

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
    Abstract: Abstract 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 vertebra. 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 plausible shapes. Results 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. Conclusions 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 accurately.

  • 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.