2.1 Materials
This study used CT models of GE LightSpeed 16 slices CT and GE BrightSpeed 16 slices CT with rotation time of 1 second, section thickness of 0.625 mm, pitch 0.562:1, dose 120 kV, 250mA. Scan section parallel to the base of the skull, and scan field covers the entire mastoid air chamber. We collected cross-section images of 11 out-patients, in which 10 as training group and 1 as testing group.
2.2 The creation of a database
The atlas of the training database was established by manually drawing the boundary of three small ear bones in the middle ear. The number of these feature points was not fixed, but such feature point must be an obvious form of representation, such as turning point. Select the feature point by counter-clockwise, one by one, and make records as training samples to facilitate further analysis. The height of middle ear is about 1 centimeter, so it appears 21 sections in the CT. These training samples were then classified and stored according to their CT location. Each section included the manually circled information of middle ear boundary of 10 patients, which is defined as follows:
Where l stood for the section number ( 1 ≤l ≤L ),m stood forthepatientnumber(1 ≤ m ≤M ),jisthethreesmallearbonesnumber(1 ≤ j≤3 ),and N istheboundary length of an unfixed size.
2.3 Identification of middle ear
Middle ear mainly consists of three small hearing bones. It is usually represented by only a few pixels in high-resolution CT, and even appears as 2 to 3 indistinct pixel widths in some cases. So, computer automated detection would be difficult without anatomical knowledge or training samples!
There are different shapes of skull due to variation of the human body, and this results in different locations and shapes of the skull on CT images. Therefore, identification of the middle ear is divided into two steps; firstly find out the rough position of middle ear, and secondly identify the accurate boundary of three small hearing bones.
Cross-correlation is often used to find the same or similar signals. The bones in middle ear may be divided into two or even three pieces in several sections of training samples. Since the scope of these small objects is quite small, it can not be directly calculated by using the cross-correlation between them. As a result, we firstly roughly find out the similar position in a large area and find out the relative boundary in testing image, then revise it according to the relative relationship between the blocks and the area. Finally the best deformation parameter of the block would be obtained.
Cross-correlation method is applied in the two steps of recognition of the middle ear to find similar objects. Such method is described as follows:
First algorithm: identification of the location of the middle ear
Manually select the first CT scan image in which the middle ear appears from the test samples, and select the information of certain section ( l ) from training samples based on theaboveimage.Each section includestraining atlasof10 patients’image data of their middle ears. This atlas includes boundary and image data of middle ears of those patients.
a. Selection of training samples: the training sample size, determined by the manually selected boundary coordinates of the middle ear in the section, is described as follows:
， 1 ≤ j ≤3
Width and height of the training samples, upper-left corner coordinates is (xmin, ymin), Tm symbolizes the training sample.
b. search space: in each section, remove the part where existence of the middle ear is impossible in the training atlas, and the rest would be the search space. Take the left ear for example, the image is segmented by a middle line, then we divide the left
and the left-middle segment is the search space shown in Figure 2.
Figure 2: The area surrounded by white line is the search space.
C. Search for the position of middle ear
Find out the position of the middle ear with training samples using cross-correlation in the search space of testing images of each section.
(x, y) is the coordinate points of the search space. We can obtain one largest value of cross-correlation in the search space of the training atlas using any of the training samples of each section , which is the most similar part between two areas. As a result, we can find out the corresponding training samples by comparing the maximum cross-correlation values, namely:
The problems here are three. The first is that the value of three middle ear bones in CT images is not very high compared to the skull next to them. The value of the points multiplied would be low and we may get false results more easily. The second is that errors may occur since the area size we selected in each training sample is not always the same. The third is that the size of the middle ear is not big, and there will be many similar parts in the whole figure, making results prone to influence.
Solution to the first problem is making the sum of each figure the same when carrying out the calculation, which is have it divided by sum of these training samples and then multiplied by a fixed value. By this way the sum of two figures will be equal.
Then the lighter figure and the darker figure can be adjusted, leaving only the difference of gray value between two figures.
As for the second problem, the solution is have it divided by the number of pixelsofthefigures,and you’llgettheaverage ofthemean.Thethird problem is difficult to solve mathematically, so we can only circle a larger area to get more information for comparison, and adjust coordinates using vector after finding them out.
The above are process for identifying the location of the middle ear, which is a crucial step. As long as we can successfully find out the similar points in this step, then the errors can be minimized when we search for the boundary of the middle ear.
The second algorithm: detection of the boundary of three small ear bone
a. The best samples of three small ear bones: we can obtain the best sample after the previous step, and the three small ear bones in this sample are most similar to the training atlas. We detect the boundary of three small ear bones using this best sample.
b. Affine Transformation Model
Select the coordinates of three small ear bones from the best training samples, and we can get the corresponding samples.
We conduct the Affine transformation starting from the position in the testing image obtained in the previous step, and we can find out the optimal deformation parameters with the help of an optimized search of deformation parameters. Affine transformation model formula is as follows:
a1, a2, a3, a4, a5, a6are the deformation parameters, while (x, y), (x*, y*) are the coordinates before and after deformation.
In the optimized search, the cost function we defined was: after the two figures ( ) were respectively standardized (zero mean, one standard deviation), subtract the values of the same points of the two figures and then square it and sum it.
After obtaining optimal deformation parameters, we can obtain the three small
ear bones boundaries after substituting the parameters with the feature points of the training samples and having it transformed with Affine transformation model.
c. Smoothing the boundary points
When we select the feature points, the selection is very sparse, making the boundary not smooth. So we make up for the missing points of boundary and smooth the boundary by using the cubic spline curve.
3. Results
Establishment of a database: the middle ear is about 1 cm in size, and we can get approximately 21 sections of the middle ear after conversion according to the CT scan resolution (0.625mm). Currently we have collected images of 10 patients with the boundary of three small middle ear bones manually selected shown as Figure 3 (b).
Since these 10 patients are training samples, we deposit the manually selected feature points into the database according to their corresponding section, and thus create a source of anatomical knowledge for subsequent analysis.
(a) (b)
Figure 3: Figure (a) is a manually selected large-block feature point, and we can define a rectangle (large block) upper-left corner point according to the minimum x and y coordinates in the selected range. Figure (b) is the manually selected feature points of three small ear bones. The selected feature points are all characterized with edges and corners with a marked turning point.
Figure 4: This is an image from training group, which shows the most similar position after cross-correlation calculation according to large-block image data of the 10 patients in the training group. Despite a slight error, it still falls within the acceptable range.
Identification of the middle ear position: the identification process of the position of the middle ear is divided into two steps because of the limited size of the middle ear, which is difficult to find out, as well as the diversity of each patient's skull size and shape. The first step is to identify the rough position of the middle ear. The system can automate the search once you input test images and select the initial section of the middle ear. First of all, the system selects the training samples from the corresponding anatomical section, then search for the most similar samples in the search space defined by the first algorithm. The results are shown in Figure 4. The rectangle in the image is the most identical region.
(a) (b)
Figure 5: (a) the three small hearing bones which have undergone deformation with the initially manually selected feature points after the optimal deformation parameters are obtained. (b) the result after the edge smoothing.
Detection of the boundary of the three small ear bone: the three vectors pointing out the positions of the three small ear bones form according to the upper-left corner coordinate points of the large-block rectangle and the coordinate points of the three small ear bone in training samples. These vectors can work as the initial values (in Affine model parameter) in the detection of the three small ear bone boundary in the performance of the displacement. The three initial values of are the rotation matrix with respective rotation angles of . Although increasing initial values also increase the computing volume, the possibility of falling into the local optimal traps reduces to a certain degree. With deformation of the Affine model, we get to find out three small ear bones of different shapes, and thus increase the accuracy of boundary detection. Figure 5 (a) is the preliminary results of the second algorithm, Figure 5 (b) the results after edge smoothing.
(a) (b)
Figure 6: The results of reconstruction of the three-dimensional image; (a) (b) are images from two different angles.
Three-dimensional reconstruction of three small ear bones: gradually find out the boundary of the three small ear bones in 21 sections in the testing group, turn them into files which can be recognized by software 3D doctor, then present the three-dimensional images using volume rendering method as we can see from Figure 6.
4. Discussion and conclusion
The system us based on knowledge of anatomy and imaging data. The system can automatically analyze and identify the boundary of the three small ear bones, and conduct three-dimensional reconstruction once users enter the sections of three small ear bones. The three-dimensional structure of the three small ear bones can then be
displayed on the computer screen, facilitating the preoperative and post-operative evaluation for physicians. It’s time-consuming to establish training samples of database, but once the database is successfully established, the subsequent analysis can then be automated and significant cost of manual drawing by physicians can be reduced by computerization. In this study, we still need more patients included in the training and testing groups to ensure the availability and accuracy of the system.
Because CT image is two-dimensional data, which is difficult to visualize its three-dimensional structure, this study can not only help reduce the workload of physicians, but also help educate and train the inexperienced physicians at the same time. In this study, the problem of overlapping boundaries of three small ear bones still remains, and we will focus on overcoming this shortcoming in the future.
5. Thanks
This study was sponsored by the China Medical University Hospital, project number:
DMR-97-088.
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