Introduction
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Obtain the best possible segmentation results.
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Achieving a fast operation of all the methods used.
Materials and Methods
Image Dataset Used
Detecting and Segmenting Microcalcifications in Mammograms
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Microcalcifications are small, from 0.1 to 1.0 mm. Their average size is 0.3 mm. Microcalcifications smaller than of 0.1 mm also occur and are often impossible to distinguish from high-frequency noise.
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Microcalcifications can differ in their shape, size, and the distribution within the mammary gland.
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They are characterized by a low contrast in mammograms.
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Sometimes they adhere closely to the tissues surrounding them.
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Morphologically detecting microcalcifications.
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Watershed segmentation of microcalcifications.
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Malignant microcalcifications appear to be small, numerous (>5 concentrated on an area of 1 cm2), and distributed densely because they lie inside milk ducts and associated structures in the breast.
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Benign microcalcifications are generally larger, less numerous (<4–5 per 1 cm2), and more spread out because they form in the breast stroma, cysts, or benign masses.
Morphological Detection of Microcalcification
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Stage 1. The input mammogram marked I should be subjected to an operation of shifting it 21 gray levels down and then the same number of gray levels up in order to remove small brighter points in the darkest parts of the image, which could be wrongly recognized as microcalcifications. As a result of these operations, the variance of the image for gray levels between 0 and 21 will be removed. The output image is marked as I 2.
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Stage 2. The second stage is about detecting microcalcifications of various sizes using the morphological pyramid and a structural element of the constant size of 3 × 3 pixels. The first level of the pyramid is the source image. The second level is obtained by applying first the closing-opening (C-O) filtration [26] with the aforementioned structural element to the source image, and then sampling every second pixel from the image. The third level is produced by conducting the same operations on the second level image. The C-O filtration and sampling produces an image size reduced twice but with the useful information about its objects retained. Microcalcifications are detected at the second and third levels of the pyramid, using the following formula:$$ T=I- min\left\{{\gamma}_S\left[{\varphi}_S(I)\right],I\right\} $$(1)where I is the input image, T is the output image, S is a square structural element 3 × 3 pixels in size, γ S and φ S are, respectively, the opening and closing operations [26], and min represents the point minimum. The operation (1) detects small brighter parts of the image (Fig. 3b, c). Pixels with a less irregular brightness distribution in their surroundings receive a higher value. This transformation also constitutes de-noising filter. The min operation ensures that the result will never be negative.After the microcalcification detection at the second and third levels of the pyramid, the results are subjected to thresholding with the threshold equal to 4, i.e., pixels with their gray level below the threshold are assigned the value of 0 and the pixels with a gray level equal to 4 or higher are assigned the value of 255. If the threshold value was set lower, e.g., at 3, this produced too many potential microcalcification signals. The results of thresholding at the second and third level of the pyramid should then be reduced to the dimensions of the input image and sum up using the logical OR operator. The size of the input image can be restored by replacing every pixel with a block sized 2 × 2 for the second or 4 × 4 pixels for the third the pyramid level.
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Stage 3. The third stage consists in extracting all the brighter areas found in the I 2 image produced in stage 1. This will be done by the morphological operation of the extended maximum emax [26], where image I 2 is the mask and the image I 2 after the number 5 is subtracted from all of its pixels is the marker:$$ {I}_{emax}={T}_1\left[h- convexit{y}_5\left({I}_2\right)\right] $$(2)The I emax image is composed of both microcalcifications and other brighter areas of image I 2 (Fig. 3d). In the experiments forming part of this project, the value of h was adopted as 5 because higher values made the bright area too large. However, in some cases, the image will contain excessively large areas that do not correspond to the physical dimensions of microcalcifications. Such areas must be removed from the image as part of a separate operation. It was decided to eliminate potential signals of microcalcifications inside which a vertical, horizontal, left diagonal, or right diagonal chord 50 pixels or less in length can be drawn. These objects are deleted using erosion carried out separately for every one of four linear structural elements lying along the above directions. Erosion results should be summed up logically. The summed up erosion results will serve as a marker for the reconstruction by dilating large regions from the I emax image. The I emax image will be the mask in this reconstruction. The result of calculations at this stage is the difference between the I emax image and the image produced by the reconstruction.
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Stage 4. The purpose of the last stage is to extract the area occupied by microcalcifications detected using Eq. (2). This will consist in reconstructing the appropriate areas of image I emax indicated by signals detected at the second and third levels of the morphological pyramid. The logical overlap of the image indicating the microcalcifications at the given level of the pyramid and the I emax image will constitute the marker in the reconstruction. The reconstruction results from the second and third levels of the pyramid should then be summed up using the logical OR operator, and as a result the so-called microcalcification “map” should be produced (Fig. 3i).
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Removing potential microcalcification areas located close to the edge of the image using the reconstruction.
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Removing potential microcalcification areas smaller than 10 pixels and larger than 70 pixels in area by area opening [26] and the logical subtraction of the images.
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Closing holes in image objects.
The Watershed Segmentation of Microcalcifications
Methods of Measuring and Assessing Microcalcification Segmentations Carried Out
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M denotes regions of microcalcifications identified by the computer method, while |M| is the number of pixels.
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E represents areas of microcalcifications traced by the expert—a breast radiologist, while |E| is the number of pixels in the traced regions.
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|M ∩ E|, |M ∪ E| represent, respectively, the number of pixels in the common area and the number of all pixels in the M and E regions.
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If the computer method identified a microcalcification in the GTA area correctly, it was classified as true positive (TP).
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If the computer method did not identify a microcalcification in the GTA area correctly (the microcalcification does not occur in the area marked), it was classified as false positive (FP).
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If the computer method did not indicate a microcalcification in the GTA area even though it was there, this represented a false-negative case (FN).
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If the computer method produced a microcalcification signal outside of the GTA area, this represented a case of FP.
Selecting Parameters in Computer Method
Parameter | diff | Th | h | nPxls | minPxls | maxPxls |
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Value | 21 | 4 | 5 | 50 | 10 | 70 |
Results and Discussion
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The number of ROIs depending on the false positive per image (FPI) examples obtained (there are altogether 200 ROIs).
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The mean sensitivity values of detected microcalcifications depending on the detected false-positive (FP) examples.
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Standard deviations (SD), minimum values (min), and maximum values (max).
SI | OF | OV | EF | SI | OF | OV | EF | ||
Mean | 0.831 | 0.781 | 0.735 | 0.174 | Mean | 0.780 | 0.733 | 0.682 | 0.223 |
SD | 0.104 | 0.080 | 0.091 | 0.142 | SD | 0.123 | 0.109 | 0.101 | 0.204 |
Min | 0.531 | 0.482 | 0.395 | 0.018 | Min | 0.432 | 0.415 | 0.341 | 0.021 |
Max | 0.952 | 0.902 | 0.842 | 0.583 | Max | 0.924 | 0.865 | 0.825 | 0.653 |
Benign: computer method versus expert | Malignant: computer method versus expert | ||||||||
SI | OF | OV | EF | ||||||
Mean | 0.805 | 0.757 | 0.708 | 0.198 | |||||
SD | 0.113 | 0.094 | 0.096 | 0.173 | |||||
Min | 0.432 | 0.415 | 0.341 | 0.018 | |||||
Max | 0.952 | 0.902 | 0.842 | 0.653 | |||||
Benign and malignant: computer method versus expert |
FPI | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Number of ROIs | 24 | 36 | 32 | 34 | 20 | 8 | 12 | 22 | 12 |
Mean sensitivity | 0.781 | 0.793 | 0.813 | 0.818 | 0.808 | 0.806 | 0.804 | 0.798 | 0.776 |
SD | 0.116 | 0.154 | 0.143 | 0.153 | 0.108 | 0.04 | 0.042 | 0.052 | 0.062 |
Min | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.666 | 0.666 | 0.5 | 0.5 |
Max | 1 | 1 | 1 | 1 | 1 | 0.85 | 0.857 | 0.857 | 0.857 |
I | II | M | |
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Mean | 0.514 | 0.321 | 0.836 |
SD | 0.04 | 0.021 | 0.051 |
Min | 0.420 | 0.312 | 0.730 |
Max | 0.552 | 0.399 | 0.951 |
MAC | GAC | M | |
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Number of ROIs | 128 | 1000 | 200 |
Size of ROI in pixels | 81 × 81 | From 20 × 20 to 41 × 41 | 512 × 512 |
Mean OV: benign cases | – | 0.55 | 0.735 |
Mean OV: malignant cases | – | 0.49 | 0.682 |
Mean OV: malignant and benign cases | 0.61 | 0.52 | 0.708 |
Mean time in seconds for a single ROI | – | – | 0.836 |
Mean time in seconds for a single microcalcification | 0.42 | 0.4 | – |
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In all experiments done on 200 ROIs 512 × 512 pixels in size, the average values of the SI, OF, OV, and EF indices amounted to, respectively, 80.5, 75.7, 70.8, and 19.8%. Higher values of SI, OF, and OV indices and a lower value of the EF index were obtained for benign cases, which are relatively larger and less numerous than malignant ones. The values of the SI, OF, OV, and EF indices for 100 analyzed ROIs containing benign lesions are 83, 78, 73.5, and 14%, while for those with malignant lesions they equal 78, 73, 68, and 22%. In [9], only the OV index was analyzed, and just as here, higher values were obtained for benign lesions than for malignant ones. In [8], in turn, only the sizes of microcalcifications were distinguished, and no results of experiments for types of microcalcifications are presented. This study produced higher average values of the OV index than in [9] (52%) and in [8] (61%). However, it is worth noting that Duarte et al. [9] researched 1000 ROIs from mammograms from the DDSM database, so significantly more experiments were carried out than in this publication (altogether 220 ROIs, with 20 used to determine the parameters of the method, and tests carried out on the remaining 200). What is more, in [9], the researchers analyzed various types of microcalcifications and for different types of breast tissues according to their classification to four tissue density categories [37]. In this study, two types of microcalcifications were analyzed, namely those which are symptoms of malignant cases and those which represent benign cases, and they are generally fatty breast cases. Unfortunately, as the manual tracing of individual microcalcifications can be very time consuming for the expert (as long as 30 min for a single ROI), this forms an obstacle to conducting a large number of experiments and significantly prolongs their time. In [8], 128 clusters of microcalcifications were analyzed.
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According to the data from Table 3, there were eight supposed microcalcifications at the most. In the experiments completed, the most frequent ROIs had one, two, and three supposed microcalcifications, and for these cases the standard deviations are the greatest. The minimal number of microcalcifications that occurred was 5 and the lowest value of the standard deviation can be observed for this group. The mean sensitivity in all the experiments amounted to 80% and reached the maximum value of 81% for FPI 2 and 3. On the contrary, the lowest value of 77% occurred when the maximum number of FPI signals was equal to 8. The most frequent cases which reduce the mean sensitivity of the method are those where few microcalcifications occur in the mammogram but are not all detectable by the computer method. For example, there are three microcalcifications in Fig. 8b, but the computer method missed one microcalcification—Fig. 8c, so its sensitivity amounts to only 0.66. This relationship becomes vague when there are more microcalcifications, and then omitting a few of them does not significantly impact the sensitivity values obtained. The appropriate examples are illustrated by the following pairs of Fig. 8e and f as well as Fig. 9b and c. Figure 8e contains five microcalcifications, so not detecting one of them yields the sensitivity of 0.8—Fig. 8f. In the example from Fig. 9b, the radiologist has found 11 microcalcifications, and if the computer method misses two, the sensitivity amounts to 0.81. Figure 9e, in turn, contains nine microcalcifications, so if the computer detection misses three, this represents the sensitivity of 0.66. According to the data from Table 3, sensitivity falls to 0.5 in the worst case and is equal to 1 in the best case, which means that all microcalcifications had been found.
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The average completion time of all steps of the computer method for ROIs 512 × 512 pixels in size amounted to 0.83 s and consisted of 0.51 s for the morphological detection of microcalcification and 0.32 s for the watershed segmentation. In comparison, the authors of [8] analyzed ROIs 81 × 81 pixels in size and reported that the average segmentation time of a single microcalcification was 0.42 s. Duarte et al. [9] also give the average segmentation time for a single microcalcification, which amounted to 0.4 s for analyzed ROIs whose dimensions ranged from 20 × 20 to 41 × 41 pixels. It should be noted that the active contour methods presented in [8, 9] require a manual initialization for every single microcalcification, which represents a significant limitation because it prolongs the segmentation process, particularly if a large number of ROIs is analyzed and they contain an even greater number of microcalcifications. In summary, the solutions proposed in this publication are more practical because they do not require initializing in every instance—they allow the segmentation process to be automated not just for single microcalcifications but for many at the same time, inside ROIs larger in size and within a shorter time; and they do not require initializing in every instance—they allow the segmentation process to be automated not just for single microcalcifications but for many at the same time, inside ROIs larger in size and within a shorter time.