1. Ant colony segmentation approach for volume delineation in PET.
Mohamed Hafri1, Dimitris Visvikis1, SeniorMember IEEE,Hadi Fayad1,2,Member IEEE
1 INSERM UMR1101, LaTIM, Brest, France, 2 Université de Bretagne Occidentale
Objectif :
Proposing a novel volume delineation approach of PET images based on the foraging behavior of ants.
Introduction
Producing highly conformal radiation dose to the tumor in PET guided radiation treatment therapy is based on the accurate FTV (functional tumor volume) delineation.
However, accurate volume delineation (segmentation) is very crucial task due to the low spatial resolution and the presence of noise in PET images.
Novel metaheuristic segmentation model based on the low level interaction of ants during foraging, has shown promising results in image segmentation.
The concept of the model consist on the ants exploration of the image searching for tumor pixels and communicating with each other using pheromones.
The efficacy and robustness of the proposed model were validated on phantom images, where it has produced segmentation map very close to the ground truth.
Materials and Methods
1. ACO model
Update pheromone rule:
At the beginning of the ACO algorithm, all the image pixels are initialized with the same quantity of pheromone “η”
At each time step a certain pheromone quantity is laid depending on the degree of similarity between the food source and the occupied pixel.
is the homogeneity based component, used in fuzzy connectedness algorithm[3]
is the grey level average intensities of the neighboring voxels of “o”
The pheromone update rule at the pixel “i” in the iteration “t” is defined as:
Binarization:
The output of the ACO model is a pheromone image which will be binarized using the median value of the image.
2. Phantom study:
Seven 3D simulated tumors with variable levels of irregular shape and homogeneous or non-homogeneous uptake distributions were used in this study.
3. Classification error:
The criterion of comparison we used in this study is defined as follows[4]:
Define the food source
Ants move in the image
Update the pheromone image
Tumor
Binarized image
Iterative process
Defining Food [1]:
The food source is the reference object that ants use to search for similar pixels.
Simple representation of food was proposed by [1].
we select the r radius neighborhood of a pixel “o” in the image manually as it is
illustrated in the figure, for example if (r=3) we select the 26 neighboring voxels.
Transition rule:
The state of an individual ant is described by it’s position “p” and orientation in two
axis θ1 and θ2.
At each time step the ant will go from one pixel to another. The choice of the new pixel must take into account:
(I). the pheromone quantity of all the neighboring pixels, (II). the visibility of the next pixel, ensure that the ants have higher probability to continue walking in the same direction of the previous step, and (III). finally, the image pixel can only be occupied by one ant. The probability of an ant to go from pixel “i” to “j” is defined as follow [2]:
is the pheromone weighting function, measuring the relative probabilities of ant “k” moving to the pixel “j” having a pheromone density σ.
controls proportionally the influence of pheromone trail in deciding the future destination,
is the sensory capacity, used to decrease the ant's capability of sensing the pixels of high pheromone concentration.
is the weighting factor, where is the change of orientation it ensures that the bigger orientation changes are less likely than small ones.
This error measurement takes into consideration the spatial distribution of the tumor by considering both background voxels classified as tumor and tumor voxels classified as background.
Values of w(∆) for all neighboring voxels for an ant, it’s previous direction is north forward.
Results
Tumor
ACO
FLAB 1
4.17%
5.29% 2
10.59%
17.58% 3
2.92%
2.94% 4
1.90%
1.42% 5
4.87%
9.59% 6
1.70%
1.73% 7
5.23%
5.41%
The performance of the ACO model was compared with Fuzzy Locally Adaptive Bayesian
Model [4]
Number of iteration 30, number of ants is 30% of the images pixels put randomly.
ACO led to segmentation maps close to the ground-truth (mean percentage error of 4.48±3.03%) compared to (6.28±5.71%) for FLAB
- explained by the pheromone update rule which reduces the impact of intensity fluctuations and renders it robust to noise.
Tumor
Ground truth
FLAB
ACO
Conclusions
In this paper, we proposed a novel functional tumor volume segmentation approach based on the behavior of ants during food searching. The performance of the developed model on phantom images was very promising. Future works will be dedicated to optimization of the ACO parameters, incorporating the fuzzy model into the pheromone laying rule, extend the model to work on 3 tumor classes for the delineation of inhomogeneous tumors. In addition the proposed algorithm will be exploited for other applications such as 4D PET kinetics modeling.
[1] Peng Huang, et al An artificial ant colonies approach to medical image segmentation, Computer Methods and Programs in Biomedicine, v.92 n.3, p , December, 2008
[2] Dante R et al“How Swarms build Cognitive Maps” In Luc Steels (Ed.), The Biology and Technology of Intelligent Autonomous Agents, (144) pp , NATO ASI Series, 1995.
[3] P.K. Saha, et al, Scale-based fuzzy connected image segmentation: theory, algorithms, and validation, Computer Vision and Image Understanding 2002, 77, 145–174.
[4] Hatt M, et al“A fuzzy locally adaptive Bayesian segmentation approach for volume determination in PET” IEEE Trans Med Imaging. 2009, 28(6):