1. Introduction

2. Materials and Methods

2.3. Methodology structure and implementation

In grayscale images, the intensity increases as the pixel value approaches 255, which represents white. This value is determined by the fact that each pixel is represented by an 8-bit binary value, which, when converted to decimal, can range only from 0 to 255. The platform utilizes the Local Thresholding method to account for the noise and undefined areas commonly present in ultrasound images. This method involves selecting regions ($block\_size$) around each pixel in the input image to determine its value based on a defined method and parameter ($param$). In the "Gaussian" method, a specific sigma value is utilized, whereas in the "generic" method, a function object is employed to calculate the threshold for the center pixel. This calculation is based on the flat matrix of the local neighborhood, as specified in Equation 1.

$$threshold\_local(image,block\_size,method,param),$$

(1)

Figure 5 displays various images where local thresholding was performed on different regions. The images show how regions with greater intensity are distinct and separated from other areas where there are no grooves or bones.

In all the utilized methods, a cropping operation is performed on the designated groove area, followed by a pre-processing step for the segmented region. This pre-processing involves scaling and adjusting the maximum and minimum pixel values of the obtained images. The largest pixel value is normalized to 1, while the smallest pixel value is normalized to 0. For the remaining pixels, a scaling function is applied, where each pixel in the image is subtracted by the minimum value and divided by the difference between the maximum and minimum values within the clipped image represented in Equation 2.

$$image=(im{g}_{crop}-np.min\left(im{g}_{crop}\right))/(np.max\left(im{g}_{crop}\right)-np.min\left(im{g}_{crop}\right)),$$

(2)

The purpose of doing this is to distinguish between the structures and the background, as well as the noise present in the image, which are generally darker than the grooves that have values close to 1. An example of the results is depicted in Figure 6.

There exist multiple methods to enhance the contrast between the background and elements in ultrasound images. One of such methods is Sigmoid correction, also referred to as Contrast Adjustment (Equation 3).

$$skimage.exposure.adjust\_sigmoid(image,cutoff=0.5,gain=10,inv=False),$$

(3)

Equation 4 illustrates the Sigmoid Correction, which performs a pixelwise transformation on the input image, scaling each pixel to the range of 0 to 1.

$$O=1/(1+exp*(gain*(cutoff-I)\left)\right),$$

(4)

The $cutoff$ parameter determines the cut-off point of the Sigmoid function, shifting the characteristic curve horizontally. The $gain$ parameter represents the constant multiplying factor in the power of the function. Additionally, the $inv$ parameter controls the behavior of the correction: when set to False, it returns the Sigmoid correction, and when set to True, it returns the negative Sigmoid correction.

The overall contrast of an image, particularly in the case of ultrasound images, can be improved by applying various treatments that enhance the contrast between the elements and the image background. One such method is the Sigmoid correction, which is also referred to as Contrast Adjustment.

Adjusting the cutoff contrast factor and the gain value can control the overall contrast enhancement by regulating the amount of brightening and darkening. While the default values for cutoff and gain are 0.5 and 10, respectively, they may not always be optimal for the images under consideration. Therefore, several modifications need to be made to determine the best cutoff and gain values that maintain the structure of the grooves while eliminating noise in the surrounding areas. It has been observed that a cutoff value of 0.4 combined with a gain value between 10 iterations to eliminate some of the noise around the groove without modifying its structure. Figure 7 illustrates an example comparing the original image with the result obtained after applying the sigmoid function.

In image processing, erosion reduces bright regions and enlarges dark regions by setting the pixel value at (i, j) to the minimum over all pixels in the neighborhood centered at (i, j). Conversely, dilation enlarges bright regions and reduces dark regions by setting the pixel value at (i, j) to the maximum over all pixels in the neighborhood centered at (i, j). In the platform, both operations are used in a function called "closing" represented by Equation 5. This function performs greyscale morphological closure of an image by applying dilation followed by erosion. It effectively removes small dark spots and connects small bright cracks. This operation is useful for closing dark spaces between bright features in the image. The function takes the image and the trace (expressed as a matrix of ones and zeros) as parameters.

$$closing(image,footprint=None,out=None),$$

(5)

Figure 8 illustrates an example of the application, demonstrating how a group of initially connected structures is merged together to achieve a segmentation result that closely resembles the intended structure.

After binarizing and applying the closing function to the ultrasound image, the identification and characteristics of each structure are obtained using two functions from the Python library skimage.measures: label and regionsprops. The label function takes the image to be labeled ($labe{l}_{i}mage$) as input and optionally accepts a parameter called $retur{n}_{n}um$. When $retur{n}_{n}um$ is set to True, the function returns the number of regions found as an integer. The output of this function is an image and an optional integer value.

$$label\_image,nregions=label(image,return\_num=True),$$

(6)

The labeling function (Equation 6) is employed for structure recognition and labeling, but it does not provide detailed information about individual regions, such as their area, centroid, etc. For that purpose, the regionprops function is an algorithm that returns a list with the same number of elements as the number of structures detected in the $label\_image$ (Equation 7). Each element in the list contains a dictionary with various characteristics of the corresponding structure, such as area, coordinates, centroid, etc. Then, a histogram is used to determine the number of structure based on their area (Figure 9).

$$props=regionprops\left(labe{l}_{image}\right),$$

(7)

Moreover, a method for defining the image furrows is to use the morphsnakes library based on a Morphological Active Contours without Edges (MorphACWE) method [25]. This technique is particularly useful for segmenting objects in images and volumes with indistinct edges called. It can handle scenarios where the interior of the object is either brighter or darker than the surrounding background. Additionally, it is robust against noise and can operate on images without the need for pre-processing to enhance object contours. Upon execution, the function generates a mask of equal dimensions as the input image, which can then be used for segmentation. However, it has been observed that this function may produce errors, as sometimes the path is designated with a value of 0 instead of 1, which can hinder segmentation. Figure 10 illustrates an example that demonstrates how to address the issue of errors caused by assigning a value of 0 instead of 1 to the path in the segmentation process. By checking if the percentage of values equal to 1 in the masks is greater than 50%, and inverting them if True, this approach helps overcome the problem.

The segmentation process categorizes an image into segments or extracts contours to detect edges. These segments represent regions with similar color intensity or other characteristics, while neighboring regions have distinct features. In many cases, visualizing the entire region is unnecessary, and highlighting the contour in a specific color (e.g., red) suffices for structure identification in the original image. The $skimage.segmentation$ library offers the slic function, which employs k-means clustering for image segmentation. This function requires input parameters such as the image to be segmented, the initial number of labels, an optional mask to limit superpixel calculation to specific areas, and the start label. Equation 8 represents the function:

$$m_{slic}=segmentation.slic(img,n_{segments}=2,mask=mask,star{t}_{label}=1),$$

(8)

Figure 12 demonstrates the process and outcomes of the slic function. It includes the original image, the corresponding mask, the number of segments (e.g., 10) used, and the resulting image segmentation. The image and mask are adjusted to align with the structure, allowing the grid (indicated by the yellow line in the third image) to adapt and conform to the structure’s contours. The segmentation of the structure is represented by the red line in the fourth image.

Figure 11. Example of the original image, the corresponding mask, the number of segments (e.g., 10) used, and the resulting image segmentation.

Figure 11. Example of the original image, the corresponding mask, the number of segments (e.g., 10) used, and the resulting image segmentation.

3. Experimental case of use and results

Figure 12. Result of the manual segmentation of each groove defined in the upper cards and carried out by the platform algorithms, in this case Threshold.

Figure 12. Result of the manual segmentation of each groove defined in the upper cards and carried out by the platform algorithms, in this case Threshold.

4. A comprehensive discussion of the segmentation results

5. Conclusions

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