The present invention is directed to a method for corpus callosum segmentation in magnetic resonance (MR) brain images. Embodiments of the present invention are described herein to give a visual understanding of the segmentation method. A digital image is often composed of digital representations of one or more objects (or shapes). The digital representation of an object is often described herein in terms of identifying and manipulating the objects. Such manipulations are virtual manipulations accomplished in the memory or other circuitry/hardware of a computer system. Accordingly, is to be understood that embodiments of the present invention may be performed within a computer system using data stored within the computer system. For example, according to various embodiments of the present invention, electronic data representing a target MR image, as well as electronic data representing training images for an active shape model are manipulated within a computer system.
The segmentation method of the present invention locates a boundary of the corpus callosum (CC) in sagittal MR images. According to embodiments of the present invention, this method utilizes an Active Shape Model (ASM) which is adjusted by confidence weighting boundary movement. An ASM is a statistical model of the shape of an object (e.g., the corpus callosum) which is iteratively deformed to fit the object in a current image. An ASM is generated based on training data, and incorporates prior knowledge about the object shape.
The contour of an object, such as the CC, in 2 dimensions can be described by a set of node points (x1, y1), . . . , (xn, yn). Each node point is a pixel in the image, and the set of node points define a contour which represents the boundary of the object. The coordinates of these nodes are grouped into one vector:
X=(x1, y1, . . . , xn, yn)T. (1)
In order to train the ASM on training data, a set of contours X1, . . . , Xm are manually labeled, and are then aligned to a template contour The template contour can be any one of the contours X1, . . . , Xm.
Φb represents the variation to the mean shape
and b is a shape parameter which weights the principal eigenvectors. Accordingly, any object contour can be modeled as follows:
X=M(s,θ)|{circumflex over (X)}+Xc, (2)
where {circumflex over (X)}=
represents every node in the vector {circumflex over (X)}. s denotes the scaling factor, and θ denotes the rotation angle, thus M(s,θ) represents a 2×2 scaling and rotation matrix. Xc=(x1c, y1c, . . . , xnc, ync) represents a translation vector. These parameters are described in greater detail in T. F. Cootes et at, “Active Shape Models—Their Training and Application,” Computer Vision and Image Understanding 61(1), pp. 38-59, 1995, which is incorporated herein by reference.
In addition to the shape model described above, an appearance model is also constructed to describe the image structure of the object in the training stage. In order to generate an appearance model, a grey profile is generated for each node point of each training contour by sampling around each node along the direction perpendicular to the object boundary. k pixels are sampled on both sides of each node point in the perpendicular direction, which gives a profile of length 2k+1 for each node point on a contour. The appearance model uses the normalized first derivative of the intensity of these samples pixels, which can be described by a vector gi,j of length 2k+1, where i denotes the index of a node in a contour, and j denotes the index of a contour in the training set. The appearance model is described in greater detail in T. F. Cootes et al., “Active Shape Models—Their Training and Application,” Computer Vision and Image Understanding 61(1), pp. 38-59, 1995, which is incorporated herein by reference.
The shape and appearance model generated from the training data can be used to fit a contour on an image to define a boundary of an object in the image. Given an initial contour on the image, adjustments are estimated which move each node on the contour to an improved position. The improved position d for a node i can be defined as the point decreasing the following Mahalanobis distance metrics,
f(gd)=(gd−
where
dX=(dx0,dy0, . . . , dxn, dyn). (4)
The ASM fitting process then fits the ASM of Equation (2) to the suggested new contour position X+dX The transform M(s,θ) and Xc are calculated using least square criteria to fit the mean shape
As illustrated in
At step 204, an external contour of the head is obtained in the target image. For example, a contour representing the boundary of the head can be obtained using a threshold-based region growing technique. Region growing is a technique for segmenting an object from an image. The region growing segmentation starts from a seed point and then expands the region by adding pixels with similar intensity. This is described in detail in M. Sonka et al. “Image Processing: Analysis and Machine Vision,” International Thomson Publishing, 1998, p 188, which is incorporated herein by reference.
At step 206, bounding boxes are fit to the external contour of the head in the target image and in the atlas image. At step 208, scaling and translation values are determined for aligning the bounding box of the atlas image with the bounding box of the target image. More particularly, it is determined how the bounding box of the atlas image must be resized (scaling) and repositioned (translation) in order to be the same size and in the same position as the bounding box of the target image. At step 210, the scaling and translation values are used to register the CC contour of the atlas image to the target image. Accordingly, once the scaling and translation values are determined to align the two bounding boxes, the scaling and translation parameters are applied to the CC contour in the atlas image. The transformed contour is the initial CC contour for the target image.
Returning to
Several different weighting schemes are possible to improve the CC segmentation results. According to an embodiment of the present invention, a set of fixed weight confidences can be defined based on prior knowledge. The bottoms of the genu and splenium and the middle part of the bottom of the CC body usually have blurred boundaries in the traditional ASM, so nodes located at these location can be considered “unreliable” and assigned low confidence weights. However, this fixed weighting does not take into account information from the target image data, and does not account for the fact that unreliable nodes may be different in different images.
According to another embodiment of the present invention, another possible confidence weighting scheme is to make use of the Mahalanobis distance between a node and its best fit point. In this case, if fi denotes the Mahalanobis distance between the node i and its best fit point, the weighted displacement can be expressed as
According to an advantageous embodiment of the present invention, a confidence weighting scheme can make use of the profile difference between a node and its best fit point since the profile difference describes how the structure of best fit points are similar to the node points in the training data. Accordingly, adjustments to points that are more similar to those in the training data are assigned higher confidence weights. In this embodiment, let fi=(gd−
At step 306, the ASM given in Equation (2) is fit to the adjusted contour X+dX. Scaling and rotation parameters M(s,θ) and a translation vector Xc for a registration are calculated using least squares criteria to fit the mean shape of the ASM training data to the adjusted contour X+dx. The shape parameter b is then determined to best fit the ASM given in Equation (2).
At step 308, it is determined if the contour has converged. For example, if an error value between the adjusted contour the previous contour is less than a small threshold value, it can be determined that the contour has converged. If the contour has converged, the method ends and the final adjusted contour represents the boundary of the CC. If the contour has not converged, the method repeats steps 304 and 306 until the contour converges.
Returning to
The present inventors have observed that the CC is more homogenous than the background in MR images. Accordingly, according to an advantageous embodiment of the present invention, a region-based refinement method is used to further refine the contour resulting from the ASM with confidence weighting. As described above, for each node (xi,yi), j=1,2, . . . ,n, the ASM searches for a best fit point in the normal direction with length np on either side of the contour. All of the pixels on one side of the contour are considered to be in the object, while pixels on the other side of the contour are considered in the background. The region based refinement of this embodiment searches for a point around each node in a perpendicular direction from the contour, which best divides the pixels on the profile into background and object classes. Two Gaussian models are used to model the intensity distributions of the object and the background. During each iteration of model fitting, the parameters of the two Gaussian models are estimated from the image data on either side of the nodes of the contour as follows:
where μobj and σobj are the mean and variance for the object model, and μbkgd and σbkgd are the mean and variance for the background model. Ii,j denotes the grey value of the ith pixel in the profile of the jth node point of the contour. The best fit point for node (xj,yj) is defined by maximizing the following probability:
where Gobj and Gbkgd are the object and background models, respectively, and I is a constant (I<np). In each iteration, Gobj and Gbkgd are fitted to the image data, and instead of searching for points minimizing the Mahalanobis distance, the refinement method searches for points maximizing the probability given in Equation (7). The parameter estimation and point searching steps are performed iteratively until the method converges.
The embodiments of the present invention described above are directed to a method for segmenting the CC is MR images. It is to be understood that the present invention is not limited to MR images, can be similarly applied to other medical images, such as CT images, PET images, X-ray images, etc.
The above-described method for CC segmentation can be implemented on a computer using well-known computer processors, memory units, storage devices, computer software, and other components. A high level block diagram of such a computer is illustrated in
The foregoing Detailed Description is to be understood as being in every respect illustrative and exemplary, but not restrictive, and the scope of the invention disclosed herein is not to be determined from the Detailed Description, but rather from the claims as interpreted according to the full breadth permitted by the patent laws. It is to be understood that the embodiments shown and described herein are only illustrative of the principles of the present invention and that various modifications may be implemented by those skilled in the art without departing from the scope and spirit of the invention. Those skilled in the art could implement various other feature combinations without departing from the scope and spirit of the invention.
This application claims the benefit of U.S. Provisional Application No. 60/821,763, filed Aug. 8, 2006, the disclosure of which is herein incorporated by reference.
Number | Date | Country | |
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60821763 | Aug 2006 | US |