The overall goal of this procedure is to detect subtle signs of breast cancer, in particular, architectural distortion in mammograms. This is accomplished by first pre-processing a given mammogram to detect the breast portion and remove artifacts in the given mammographic image. The second step is to detect oriented structures in the image by applying a bank of Gabor filters.
Next, the orientation field is analyzed using phase portraits to detect node like patterns that could indicate the presence of architectural distortion. The final step is to analyze all regions detected by extracting attributes or measures that characterize architectural distortion and assist in rejecting false alarms. Ultimately, the confirmed suspicious areas are presented to the radiologist for further analysis, and the efficiency of the procedure is evaluated in comparison with the results of clinical tests such as biopsy.
The main advantage of our technique over existing methods like computer rated detection of masses, is that we are able to detect subtle signs of architectural distortion without a central tumor or mass being evident. The Implications of this technique extend to the diagnosis and treatment of breast cancer. It facilitates the diagnosis of early stages of breast cancer and therefore improves the prognosis of treatment.
Visual demonstration of this method is critical. The image processing steps are difficult. There are several intricate steps that are mathematically complex.
The steps of this protocol are done using a combination of custom and packaged software. Start the procedure with a digitized mammogram downs sampled with a Gaussian filter. Segment the breast region in the image using tzu's adaptive thresholding method and identify the approximate boundary of the breast.
Next, extract oriented patterns using Gabor filters. A Gabor filter is an anisotropic band pass filter with a preferred orientation. This real Gabor filter function is oriented at minus 90 degrees.
The sigmas are standard deviations along the respective axes, and F knot is the frequency of the modulating. Sinusoid filters at other angles are obtained by using a coordinate transformation. This animation shows the impulse response of a Gabor filter on the left and the spectral or frequency response on the right note, the changes as the angle of orientation starts at minus 90 degrees and goes through 180 degrees right Sigma X and F knot in terms of tau, the full width at half maximum of the Gaussian term.
Also write sigma Y as a multiple L of sigma X.Now, tau and L control the center frequency and bandwidth of the filter and the width and length of the oriented components to be filtered in this animation. The value of tau in the Gabor filter is varied while keeping all other parameters constant. As tau is increased, the width of the Gabor function in the space domain is increased and the center frequency of the frequency response is decreased.
This animation shows the effect of the parameter L on the impulse response and the spectral response of a Gabor filter. For practical applications, appropriate values for tau and L must be chosen and multiple filters must be used. This video shows the application of 180 Gabor filters to a test image of a plant with parts oriented at several angles.
It is evident that the Gabor filter response captures the oriented components present in the image at various angles. The maximum response at each pixel over all the filter angles used is saved in a single image referred to as the Gabor magnitude response. The corresponding angle of the Gabor filter is saved for each pixel in another image referred to as the Gabor angle response.
Choose appropriate values of tau and L for mammography. Next, apply to the image a bank of 180 real Gabor filters evenly spaced over the range from minus 90 degrees to plus 90 degrees. Each filter extracts the oriented components of the mammogram in its corresponding space.
Domain direction for each mammogram generate a gab or magnitude response image using the highest magnitude response at each pixel. The final gab or magnitude response image shows high values for pixels related to oriented patterns, and thus highlights tissue structures with preferred directional characteristics. Regions with nearly the same gray levels and no oriented texture are not retained in the result.
Also, for each mammogram, generate a gab or angle response image, again, using the highest response at each pixel. This image gives the angle of the dominant oriented pattern at each pixel. The angles in this image agree with the angles of the underlying tissue structures.
Here, the Gabor magnitude response and Gabor angle response are shown side by side. The rectangles show a region of interest identified by a radiologist. Further detail is provided by these magnified views of the region of interest.
The next step is to use the Gabor magnitude response image to identify curve linear structures of interest with the non maximal suppression technique. Here, the pixels marked in white are the selected core pixels that are potential indicators or spicules or fibro glandular tissues. Now, remove core pixels associated with a strong gradient to prevent erroneous identification of structures.
This yields the curva linear structures of interest. Here are details of the same region before and after removing pixels associated with a strong gradient. Once this is done, filter the orientation field with a Gaussian filter and down sample to reduce noise and reduce the necessary computation.
The vote casting procedure in phase portrait analysis is shown here. The original mammogram is shown on the left and the related gabor angle response is shown on the right on the left. The small blue window shows the analysis window being slid over the original image window.
Positions that result in no vote being cast in the node map are skipped and not shown in the video window. Positions that result in a vote being cast in the node map are marked with a green asterisk at the corresponding position on the right at the end of the procedure, the node map contains a map of points or votes for cast, it's expected that relatively large numbers of votes will be cast at locations containing diverging or converging oriented patterns. A smoothing or accumulating filter is applied to obtain a filtered version of the node map.
Local peaks are detected in the filtered node map to facilitate cutting of regions of interest for further analysis. Now rank order the peaks in the node map according to their values. Once that is done, cut regions of interest from the original image centered at the corresponding peaks in the node map for nodes at the edges, create regions of interest that include as much of the image data as available at the specified peak location.
Begin characterization by selecting a region of interest, pre-processing it, and performing a two dimensional foyer transform. Shown here is the logarithm of the power spectrum after it has been converted to polar coordinates of frequency and angle. The angle shown in the horizontal axis ranges from zero degrees to 179 degrees.
The radial frequency on the vertical axis ranges from 0.02 millimeters to the negative one to 2.5 millimeters to the negative one with the top left corner, 0.02 millimeters to the negative one and zero degrees. Now transform the two dimensional spectrum into a one dimensional function of the spatial frequency. By integrating the power spectrum in polar coordinates over the angles for each value of the spatial frequency.
Here is the function plotted on a log scale, exclude low and high frequency regions and apply linear regression to identify the slope of the fitted line. This slope is an estimate of the power law factor beta of the fractional brownie. In motion model.
Use this to calculate the fractal dimension to compute the entropy. Return to the two dimensional spectrum in polar coordinates. Transform it into a one dimensional function of the angle by integrating it over the spatial frequency values.
For each value of the angle, normalize the function so that it sums to one. Then compute the entropy of the result. At this point, there are three measures for each.
Automatically detected region of interest, node value, fractal dimension, and entropy. Use these to characterize speculating patterns related to architectural distortion and separate them from normal tissue patterns. Develop a classifier using regions of interest classified by a radiologist.
Shown here in feature space are classifications of regions cut from labeled images during training green for false positives and blue for true positives. Also shown are the outputs of the trained classifier for the test case being analyzed. Black shows false positives and red true positives.
In this plot, the black line shows the free response receiver operating characteristic curve. When only the node value is used, it has a sensitivity of 80%with 8.1 false positives per patient. The red curve represents the results when the three features node value, entropy, and fractal dimension are used together at 80%sensitivity.
It results in 5.6 false positives per patient. In this image, the six regions of interest with the highest rankings are shown. The numbers outside the parentheses indicate the ranking according to the Bayesian classifier.
The numbers within parentheses correspond to the earlier node map ranking. Green rectangles represent true positive regions of interest. In the final stage of analysis, yellow rectangles represent false positives.
The red rectangle is the region with architectural distortion identified by a radiologist. Three of the highly ranked regions overlap with the suspicious area of architectural distortion marked by the radiologist, indicating successful detection by the procedure. After further work on optimization of our algorithms and programs, the procedures could be applied to mammograms in a clinic by incorporating a computer with our software and suitable display systems into the workflow of a radiologist.
Following our procedures, other methods could be developed to answer additional questions like how architectural distortion and breast tumors develop over time. Results of our procedures could be incorporated in radiological practice, resulting in diagnosis of breast cancer at its early stages, and therefore improve the results of treatment.
