### Title: *A Probabilistic
Approach to Tracking Deformable Patches for Image-Guided Surgery*

### Institution: Imperial College London

### Author: Osemwaro Pedro

### Year: 2011

### Abstract:

Totally-Endoscopic Coronary Artery Bypass operations, which should ideally be
entirely performed with a robotic surgical assistant, currently suffer from a
high rate of conversion to more traditional procedures, partly due to the
difficulty of identifying the coronary artery that is to be operated upon. One
solution to this problem is to guide the surgeon by superimposing models of
patients' hearts onto the images provided by the robot. Motivated by the
possibility of using motion information to (partially) constrain the
registration of the model to the images, this thesis focuses on
methods of estimating the motion of salient patches on the myocardial surface.

We begin by introducing an importance sampling algorithm for hypothesising
affine patch transformations in a particle filtering framework. The algorithm
minimises uncertainty by multiplicatively combining information from multiple
patch subregions. We devise a method for handling missing information based on
empirical evidence that suggests that certain importance sampling probability
ratios grow empirically with the number of subregions.

We then describe methods for calculating the dissimilarity between image regions
whilst taking into account specular reflections and illumination changes. We
achieve insensitivity to these effects by explicitly removing illumination
changes, tentatively masking out specular reflections, and ignoring pixel
differences that exceed a percentile of a weighted pixel difference
distribution.

Next, we investigate myocardial deformation sequence models, and propose nesting
a PCA model of the static deformations within a periodic B-spline-based PCA
model of the deformation sequences. We use this model to simulate data
sets that we can use to approximate maximum likelihood estimates of some
parameters of the particle filter components, and we describe a way of testing
whether or not particles have entered low-probability states in which they cease
to contribute useful information.