Poster
# 40
Poster |
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6th Internet World Congress for Biomedical Sciences |
Juan Gutierrez Aguado(1), Isaac Llorens i Eixea(2), Ricardo Ferris Castell(3)
(1)(2)Facultat de Fisica. Universitat de Valencia - Burjassot. Spain
(3)Universitat de Valencia - Burjasot. Spain
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[New Technology] |
[Medical Electronics & Engineering] |
[Radiology & Nuclear Medicine] |
Segmentation is commonly used to discriminate objects in a scene. Contour detection is a possible way to segment images. In grey level images, changes in the intensity values (by means of numerical derivation) give a first approximation on where are located the possible object contours, but this does not give a global description of contours, due to illumination changes or noise. As several authors have noted it, numerical derivation is an inverse problem and ill-posed in the sense of Hadammard, that can be regularized using Tikhonov stabilizers.
A snake (1) is a set of points over which energy is defined. In this energy there are two terms, one of them is the derivation and the other one is a Tikhonov stabilizer. The first term controls which feature the snake is attracted towards (in this case, this term is related to edge information). This term can be interpreted as an external force acting over each point. The second term controls the elasticity and the rigidity of snakes and depends on the relative position of points. This second term can be interpreted as an internal force. The next step is to obtain the minimal energy. Energy minimizing methods are: numerical resolution (1), dynamic programming (2), Hopfield neural nets, greedy algorithms (3) and simulated annealing.
In this paper, it is presented a B-snake, defined as a snake where points are represented by means of a cubic B-Spline (4), and the energy is defined throughout the whole curve. A greedy algorithm is chosen to minimize energy.
Once an image coming from a MRI of XR is digitised, an initial contour must be estimated around the organ of interest. This task can be performed using thresholding, region growing, or some other methods that permits to obtaining it.
The energy is defined as in eq 1,
where the internal energy is eq 2:
, and the external energy is eq 3:
.
I(x,y) represents the grey values of the image. In this work, the option has been to use chamfer distance (5) as the external energy, which determines the distance between an image point and its nearest edge. This implies a previous step of determining the image gradient. Thus, an image can be obtained with high values far from edges decreasing gradually towards the edges. This provides information about the sense of diminishing of energy.
Representing v(s) by means of a cubic B-Spline, and rewriting the energy to take into account the digital nature of the images, it is possible to apply a greedy algorithm in order to minimize the energy. Thus, the initial contour will move to adapt itself to the contour of the object of interest, where the energy reaches its minimum value.
As a first example, we present a digitised image from a TAC where the contour of a kidney has to be found. The external contour shown in figure 1, is determined by some pre-established initial control points. They will become the starting point of the whole process. On the other hand, the internal contour is the final B-snake, the result of the processing. The initialisation of the contour in these experiments has been made manually, by means of an interactive program.
In next example, a vertebra contour has to be found. To accomplish this goal, a process of minimization is applied to the initial contour shown on figure 2. The final contour obtained is shown in figure 3.
In this work it has been presented the basis of the snake and B-snake models for contour description.
Their application to medical images shows a good behaviour, giving rise to noise robust methods and allowing not acurate initialisation.
Nevertheless, the general object shape (smoothness, irregularities) must be known a priori in order to adjust correctly the energy terms.
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[New Technology] |
[Medical Electronics & Engineering] |
[Radiology & Nuclear Medicine] |
