Patent Application
20080298682
The invention relates to a method of image segmentation for delineating a structure associated with a reference structure.
The invention further relates to a system for image segmentation of a structure associated to a reference structure in an image.
The invention still further relates to a computer program for image segmentation of a structure associated to a reference structure in an image.
An embodiment of the method as is set forth in the opening paragraph is known from US2003/0069494 A1. In the known method a myocardium contour is determined for two-dimensional images obtained using magnetic resonance imaging technique. The myocardium contour is obtained according to a graph cut of candidate endocardium contours and a spline fitting to candidate epicardium contours in the absence of shape propagation. The known method further includes applying a plurality of shape constrains to candidate endocardium contours and candidate epicardium contours to determine the myocardium contour, wherein a template is determined by shape propagation of a plurality of diagnostic images of the heart.
It is a disadvantage of the known method that in order to perform segmentation of the structure, notably the myocardium, it is required to perform elaborated calculus using a-priori established shape and motion constrains for the reference structures (endocardium and epicardium), which requires substantial manual efforts.
It is an object of the invention to provide a method for segmenting a structure associated to a reference structure in an image, yielding more robust results.
To this end the method according to the invention comprises the following steps:
The technical measure of the invention is based on the insight that provided spatial delineation of the reference structure, for example the left and the right ventricles of the heart, notably obtained by an automatic segmentation, the associated structure, notably the myocardium, can easily be segmented, for example based on a simple topological model. The reference structure is identified on the basis of anatomical information, e.g. as is obtained from an anatomical atlas. The method according to the invention uses no shape and motion constrains, is applicable to two-, three- and four-dimensional data and is therefore more robust and precise than the method known from US2003/0069494 A1. It is noted that both US2003/0069494 A1 and U.S. Pat. No. 6,757,414b1 also use some probabilistic methods to estimate the appearance of the structure; however their methods are not robust with respect to outliers (noise in data), and are not well suited to magnetic resonance imaging data. The present invention achieves robustness due to the combination of the probabilistic method with the initial seeds that in a deterministic way indicate portions of the structure. On the contrary, the method according to the invention is superior, because it is a non-parametric method, and because it only eliminates the overlap between the appearance (image intensity) of the tissues of interest.
Preferably, the topological model is constructed using a-priori established assumptions, like a spatial interrelation of the structure and the reference structure. For example, a valid assumption can be based on a fact that the myocardium surrounds the left ventricle of the heart. For other organs, like lungs, kidneys, bladder and rectum other respective geometric or spatial insights can be used. Unlike per se known statistically trained models used in the art of image segmentation, the topological model is preferably not constructed from any training data and is, therefore, not biased towards the population represented in the training set. It is also noted, that the statistically trained models are expensive to obtain. In addition, because the method according to the invention is suitable to be applicable to three- and four-dimensional images, it presents an improved tool for image processing in clinical practice.
Upon an event the model representative of a spatial interrelation between the structure conceived to be segmented and the reference structure is fitted to the image, one obtains a set of initial seeds for the sought structure. Seed points are points that have fixed labels. Notably, these labels identify in a deterministic way if the point at issue belongs to the structure to be segmented. An appearance of the structure is learned from a probabilistic method thereby yielding a probability image of the structure. The probability image represents the probability values of a pixel belonging to the structure. Preferably, a nonparametric robust estimation approach that uses a fuzzy kNN classifier is used. kNN is a per se known classification algorithm. The idea is that, given a training set and a natural number k, a pattern is assigned to the class to which the majority of the k nearest patterns belong. The distance between patterns is a metric in the feature space. Preferably, a “fuzzy” variant of this algorithm is used. Each of the two training sets is represented as a histogram of image intensities. Starting from the sample to be classified, an equidistant wave is simultaneously propagated over the two histograms, until the sum of covered histogram values is at least k for the first time. Typically, the sum of covered histogram values will exceed k. It is important to allow this, because otherwise it would be unclear which of several possible training samples at the same distance should be chosen to complete the set of k nearest samples. The fuzzy kNN function would not be well-defined. But if the number of covered samples can exceed k, the function value can be (and is) defined to be the ratio of foreground training samples in the covered samples to the total number of covered samples. This histogram-based method is fast, but to lose even less time on the classifier evaluation, the function values are computed once for each of the values that can occur in the MR image and then just looked up when the function is actually applied to the whole volume. In order not to introduce a bias into the classifier, the same amount of training samples is drawn for foreground and background. It is noted that it is possible that the classical kNN switches between 0 and 1 more than once between classes. This behavior is undesirable for our application, because additional strong edges might be introduced between voxels of different classes, into the myocardium probability image. Fuzzy kNN does not have this problem improving the robustness of the method. This fuzzy kNN method is preferably applied in two stages, first to eliminate ouliers and then to obtain final estimation of the appearance. Both stages can also be implemented by other per se known computational algorithms.
Making use of the probability image and of the initial seeds, a segmentation of the structure is computed. Preferably, a method known from Y. Boykov, M.-P. Jolly ‘Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images”, ICVV, 2001 is used. More preferably, the graph cut method is adapted to fully automatically compute a segmentation of the left myocardium from the image and the seed points from the model. Graph cut method uses both edge and region based criteria is a robust method because it finds a global optimum instead of a local optimum. Preferably, a special graph is constructed, whereby each voxel in the region of interest is represented by a node in the graph. Additionally, there are two special nodes, called terminal nodes. One terminal node, the source node, represents the segmentation foreground. The other, called sink node, represents the background. Each of the voxel nodes has edges, called n-edges, connecting it to its neighborhood. Preferably, the eight-neighborhood for three spatial dimensions plus time are selected. Except for the n-edges, there are two t-edges for each voxel node, connecting the node to the two terminal nodes. The graph is a flow network. For flow networks, there are efficient algorithms for computing a minimal cut that separates the two terminal nodes. The idea of the graph cut algorithm is that this minimal cut defines a segmentation. A cut that separates the two terminal nodes must leave each node connected to at most one of the terminal edges. A voxel belongs to the class that the still connected terminal node represents. If neither of the terminal edges is connected, both possibilities represent a minimum cut.
Which segmentation corresponds to a minimal cut depends on the choice of edge weights. In the graph cut algorithm, the two different types of edge weights are used to encode two different penalty functions. Dp is a function that defines a penalty for the class membership of point p. It takes two different values, one for each possible label. Vpq defines a penalty for assigning different classes to neighboring points p and q. Separating similar points should be penalized stronger than separating dissimilar points. The penalty functions are then combined into the graph cut energy functional:
N is the neighborhood relation on the voxels, P is the set of voxels. In our application, only the voxels in the cardiac region of interest are part of P. As mentioned before, we use the four dimensional eight-neighborhood to make the segmentation consistent along all four axes of the image for greater accuracy in the presence of noisy slices. But any neighborhood can be used: two-dimensional (xy), three-dimensional (xyt or xyz) and four-dimensional (xyzt).
L={Lp|pεP}
L denotes the function that returns for a given voxel of a segmentation the value 1 for foreground and 0 for background. λε [0; 1] is a weighting factor that can be used to shift between the importance of class membership optimality and neighborhood optimality.
Each n-edge in the graph cut graph is represented by exactly one V-type summand of this functional. Every pair of t-edges is represented by exactly one D-type summand. The λ terms are pulled into the penalty functions. All possible penalties are computed and assigned to their respective weights in the flow graph. Because a minimal cut minimizes the sum of edge weights (penalties), it (globally) minimizes the graph cut energy functional.
It is noted that next to the property of the method according to the invention of it being suitable to segment two-, three- and four-dimensional images, it can easily be adapted to new imaging sequences, making it a versatile tool for fast and robust image segmentation. As an additional advantage, the method according to the invention, when applied to cardiac images, provides an improved endocardium contour, thereby still further improving the segmentation of the left ventricle.
The system according to the invention comprises:
The system according to the invention enables a fast and versatile segmentation of the structure in diagnostic images, whereby the segmentation can be performed on a broad class of images from different imaging modalities, like ultra-sound, X-ray, magnetic resonance imaging, etc. The system according to the invention also can be used for segmenting two-dimensional, three-dimensional and four-dimensional images of various kinds. Further advantageous embodiments of the system according to the invention are set forth in claims 6 and 7.
The computer program according to the invention comprises instructions for causing the processor to carry out the steps of:
The computer program according to the invention improves a workflow in a hospital environment, as it does not require sophisticated a-priori established models and can be used for segmenting a great variety of structures, provided their spatial relation to a reference structure is known. Examples of the structure versus reference structure comprise, myocardium versus left and right ventricle, esophagus versus lungs, rectum versus bladder and/or prostate gland in males, spinal cord versus vertebrae, etc. Due to the fact that the used model only employs assumptions on spatial interrelation between the sought structure and the reference structure, the computer program can easily be transformed for different anatomic areas and different imaging modalities. Further advantageous embodiments of the computer program according to the invention are set forth in claims 9 and 10.
These and other aspects of the invention will be discussed in further details with reference to figures.
| Number | Date | Country | Kind |
|---|---|---|---|
| 05111566.5 | Dec 2005 | EP | regional |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/IB2006/054452 | 11/27/2006 | WO | 00 | 5/29/2008 |
