Richard Tsai

Bio: Richard Tsai is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Surface (mathematics) & Visibility (geometry). The author has an hindex of 23, co-authored 62 publications receiving 1514 citations. Previous affiliations of Richard Tsai include Royal Institute of Technology & University of California, Los Angeles.

REVIEW ARTICLE: Level Set Methods and Their Applications in Image Science

Abstract: In this article, we discuss the question "What Level Set Methods can do for image science". We examine the scope of these techniques in image science, in particular in image segmentation, and introduce some relevant level set techinquies that are potnetially useful for this class of applications. We will show that image science demands multi-disciplinary knowledge and flexible but still robust methods. That is why the Level Set Method has become a thriving technique in this field.

Microscopic laminotomies for degenerative lumbar spinal stenosis

Abstract: In this retrospective study, we investigated 50 patients who had undergone primary lumbar microsurgical multiple laminotomy without spinal fusion for degenerative spinal stenosis There were 31 men and 19 women with a median age of 66 years (35-85 years) Thirteen patients had grade I spondylolisthesis, most at L4-L5 levels (11 of 13) Single-level laminotomy was done in 13 patients, two levels in 30, and three levels in 7 The median follow-up period was 27 months (range, 15-48 months) A standardized self-reported questionnaire was used for clinical outcome study The demographic data and clinical features of these patients were analyzed for the prognostic factors The analysis showed excellent results in 18 patients, good in 16, fair in 8, and poor in 8, whereas 30 patients reported that they were very satisfied with the surgery results, 10 were somewhat satisfied, 2 were somewhat dissatisfied, and 8 were very dissatisfied Therefore, the satisfactory rate of the surgery was higher if judged by patient satisfaction Among the parameters analyzed, the presence of neurogenic claudication (p = 0008), coexisting disease (p = 004), and the absence of motor deficit (p = 003) were associated with lower total scores In addition, longer duration of symptoms (p = 004) was associated with less improvement of back pain score, whereas the absence of motor deficit (p = 0004) was associated with less improvement of leg pain score The presence of spondylolisthesis did not affect outcomes

A multiscale method for highly oscillatory ordinary differential equations with resonance

Abstract: A multiscale method for computing the effective behavior of a class of stiff and highly oscillatory ordinary differential equations (ODEs) is presented. The oscillations may be in resonance with on ...

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Localizing Region-Based Active Contours

Abstract: In this paper, we propose a natural framework that allows any region-based segmentation energy to be re-formulated in a local way. We consider local rather than global image statistics and evolve a contour based on local information. Localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method. The presented technique is versatile enough to be used with any global region-based active contour energy and instill in it the benefits of localization. We describe this framework and demonstrate the localization of three well-known energies in order to illustrate how our framework can be applied to any energy. We then compare each localized energy to its global counterpart to show the improvements that can be achieved. Next, an in-depth study of the behaviors of these energies in response to the degree of localization is given. Finally, we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models.

The heterogeneous multiscale method

Abstract: The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.