## Deformable Contour Tracking and System Identification

#### Namrata VaswaniIowa State University

We consider the problem of sequentially segmenting (or tracking) an object or more generally a "region of interest" (ROI) from a sequence of images. Deforming contours occur either when the ROI is actually deforming its shape over a time or space sequence of images (e.g. a beating heart or ROIs in a brain MRI sequence or changing shape of brain ROIs during surgery) or due to changing region of partial occlusions on the ROI. The observation likelihood (likelihood of the image given the
contour) is often multimodal as a function of the contour, due to multiple objects, background clutter, partial occlusions, blurring or outlier noise. If the sequence is deforming fast (or frame rate is slow), it results in multimodal posteriors. In such cases, traditional algorithms that approximate a linear observer or a Kalman filter cannot be used for tracking. Instead, we use a recently introduced sequential Monte Carlo method called the particle filter (PF). Direct application of particle filters (PF) for such large dimensional problems such as deformable contour tracking is impractical, since number of particles required increases with dimension.

But in most real problems, at any given time, "most of the contour deformation" occurs in a small number of dimensions ("effective basis") while the residual deformation in the rest of the state space ("residual
space") is small (not zero). Based on this assumption, we develop a very efficient PF algorithm called PF-MT (importance sample only on effective basis and replace it by posterior Mode Tracking for residual deformation) where the PF dimension is only equal to the effective basis dimension. We will first discuss Affine PF-MT, where we used the 6-dimensional space of affine deformations as the effective basis. Next we will discuss Deform PF-MT, where use an interpolation effective basis, i.e. use deformation at a subsampled set of contour points as the effective basis". Multiple implementation issues using level set methods for this problem will be discussed. The need to change effective basis dimension and ways to re-estimate it efficiently using frequency domain techniques is discussed.
In fact, spatial spectral analysis of deformation sequences can be a new technique for system identification, recognition and change detection applications. Applications to brain image analysis will be described.

(This work was started in collaboration with Yogesh Rathi, Allen Tannenbaum, Anthony Yezzi at Georgia Tech.)

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