As in other cases of dealing with images, also in medical images, like US images, we use image processing and computer vision techniques to analyze those US images for numerous tasks.
INTRODUCTION
As in other cases of dealing with images, also in medical images, like US images, we use image processing and computer vision techniques to analyze those US images for numerous tasks. The task that this project deals with is to find boundaries in US images.
A major problem with US images is that it is characterized with a lot of noise. That fact makes it necessary to use robust and high noise immunity algorithm when analyzing US images. In this project we try to find boundaries of an object in the US image using the geodesic active contour model. By finding the object boundaries we can compute its geometric parameters like the area of cut and by doing so to the same object from different angles we can know its volume.
ABSTRACT
The geodesic active contour model comes as an improvement to the classical active contour approach ( “snakes” ).
The classical approach is based on deforming an initial contour towards a boundary of an object to be detected. The deformation is obtained by trying to minimize energy functional designed so its local minimum is obtained at the boundary of the object. This approach is not capable of dealing with images containing an unknown number of objects to be detected. Also there is a serious difficulty to find the parameters needed for this algorithm. Another fault of the classic approach is that the initial contour must be placed close to the object boundaries in order to detect the object boundaries.
By making changes in classical approach we derive the geodesic active contour model. Major changes that have been made are:
The interpretation of the problem of finding the local minimum of the energy functional to finding a minimum of distance defined on a new metric that include energy terms in it. This change enables us to use common techniques from differential geometry.
Using the curve evolution approach, which makes it possible to detect
several objects without knowing in advance their exact number.
By generalizing the edge detector we can use any edge detector we want in order to improve the algorithm a great deal.
Another advantage of the geodesic active contour model is that we can detect boundaries with high variation in their gradient including small gaps, a task that was very difficult to accomplish with the classic approach.
In addition, the algorithm does not require special stopping conditions.
THE ALGORITHM
The geodesic active contour model is based on curve evolution and on geometric flow. The curve is propagating by means of velocity that contains two terms:
Regularity and smoothness of the curve, which is, called internal force.
The curve shrinks and expands towards the boundary, which is, called internal force.
The iterative equation we implemented is:
- The curves are represented by level set of 3D function – U function. U function in our implementation was the sign function
- The edge detector –
The edge detector used in our implementation is:
– the image after a gaussian filtering.
– a constant between 0.5 and 1 determining the relationship between the
curve smoothness and the force coming from the image itself.
- “div” – the divergence operator.
- “
” – the gradient operator
THE RESULTS
CONCLUSIONS
- several objects in the image can be detected unless they are too close to each other then there will not be a complete separation between them
- Boundaries with high variation in their gradient including small gaps can be detected
- No need for stopping conditions for the algorithm
- A small object regarding to another object in the image will disappear from the detection image after a long time of algorithm run
- The parameter in the edge detector – controls the relation between the curve smoothness and the force obtained from the image
- In order to get results in reasonable time the size of the image must be approximately pixels
ACKNOWLEDGMENTS
We would like to thank the laboratory staff for their help and the Ollendorff Minerva Center fund for their support.