Name
Abstract | ||
|---|---|---|
Mathematical and statistical modeling of biological growth is an important problem in medical diagnostics. Here, we seek tools to analyze changes in anatomical parts using images collected over time. We introduce a structured model, called Growth by Random Iterated Diffeomorphisms (GRID), that treats a cumulative growth deformation as a composition of several elementary deformations. Each elementary deformation applies to a small region by capturing deformation local to that region and is characterized by a seed and a radial deformation pattern around that seed. These GRID variables--seed locations and radial deformation patterns---are estimated from observed images in two steps: 1) estimate a cumulative deformation over an observation interval; 2) estimate GRID variables using maximum-likelihood criterion from this estimated cumulative deformation. We demonstrate this framework using an MRI image data of a rat's brain growth. For future statistical analysis, we propose a time-varying Poisson process for the seed placements and a random drawing from a predetermined catalog of deformations for the radial deformation patterns. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1109/TMI.2006.891500 | IEEE Trans. Med. Imaging |
Keywords | Field | DocType |
biomechanics,brain,deformation,iterative methods,maximum likelihood estimation,medical diagnostic computing,patient diagnosis,physiological models,random processes,stochastic processes,GRID,MRI,biological growth,growth deformation,mathematical modeling,maximum likelihood estimation,medical diagnostics,pattern theoretic characterization,radial deformation patterns,random iterated diffeomorphisms,rat brain,seed locations,statistical modeling,time-varying Poisson process,Growth dynamics,growth models,growth patterns,random diffeomorphism | Mathematical optimization,Iterative method,Stochastic process,Biological growth,Statistical model,Deformation (mechanics),Medical diagnostics,Iterated function,Mathematics,Grid | Journal |
Volume | Issue | ISSN |
26 | 5 | 0278-0062 |
Citations | PageRank | References |
10 | 0.95 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulf Grenander | 1 | 308 | 80.59 |
| Anuj Srivastava | 2 | 2853 | 199.47 |
| Sanjay Saini | 3 | 27 | 4.84 |