医学图像处理笔记(6)-基于能量的分割

Image Energy representation

ROI

Outlining method

1. Manual

2. Fully automatic

3. Automated first guess then manual editing

4. Manual rough delineation the automatic refinement

Deformable models

contour/surface than change shape under the influence of image-based force fields

Discrete Dynamic Contour(DDC)

Composition of Energy Function

Structure

DDC represented by a set of ordered vertices connected by straight line segments

Coordinates

each vertex i has following coordinates at time t

\(p_{i}(t)=(x_{i}(t), y_{i}(t))\)

Forces

each vertex i has a total force acting on it



Dynamics

total force acting on each vertex i at time t causes it to accelerate





Overall algorithm

1. display image
2. allow user to initialize contour, set velocity and acceleration of each vertex to 0;
3. calculate total force at each vertex
4. calculate acceleration of each vertex
5. update position and velocity of each vertex
6. re-sample DDC
7. repeat （3）to（6 ）until all vertices stop moving

image forces
\(\vec{f}_{i}^{im}(t)\) is an image force that drives each vertex towards "features" that define boundary
derive from an "energy " that is defined at all pixels of the image:
\(\vec{f}_{i}^{im}(t) = -\vec{\triangledown} E(x_{i}, y_{j})\) 

image forces driver each vertex to closest local minima of energy field

Internal forces
\(\vec{f}_{i}^{in}(t)\) is an internal force that keeps the contour "smooth" in the present of noise in the image

noise in the image can cause DDC to become jagged, internal force keeps DDC smooth by minimizing local curvature. we cat take it to be proportional to local curvature
\(\vec{f}_{i}^{in}(t) = \vec{c}_{i}(t)\) 

\(\vec{c}_{i}(t) = \hat{d}_{i}(t) - \hat{d}_{i-1}(t)\)


                     


damping force
\(\vec{f}_{i}^{d}(t)\) is a damping force that makes the dynamical behaviour of the contour stable

with image and internal force only, DDC may ocillatte between two local minimal. viscous damping is necessary for convergence.
\(\vec{f}_{i}^{d}(t) = w^{d}\vec{v}_{i}(t)\)   -1<w<0

re-sampling

variable selection for energy function