Segmentation Approach Towards PCM Images 1133
halos at the boundaries of the flocs and filaments. Such factors are used to tune the image segmentation (Siddiqi et al., 1998; Kulkarni, 2012; Shanmugavadivu et al., 2016) to deal with artifacts specific to the application, such as halos in our case. If we observe the halos closely as shown in Figure 4, they have two edges. One is with the foreground, and the other is with the
flocs or filaments,which is comparatively sharper. Therefore, the adjustment factor seems an intuitive way to increase the threshold on the gradient to shrink the detected boundary toward the flocs or filaments. This method comprises of several steps. First, the image
is converted into grayscale image (The MathWorks, I, 2015). Second, the image is converted to gradient image using the Sobel operator in both horizontal and vertical direction. Third, the gradient image is binarized using the tuned adjustment factor. Fourth, the binary image is added to grayscale image to sharpen the edges of the filaments. Fifth, the gradient of the image with sharpened edges is determined and binarized using the threshold calculated by the default method of MATLAB, as mentioned before. Finally, the morphological operation of image closing was used using a disk shape structural element of size 2, to fill the small discontinuities.
k-Means-Based Segmentation k-Means is a well-known clustering method (Lloyd, 1982), which is required to be initialized or seeded carefully. In this method, the pixels in the RGB color space are classified into foreground and background using k-means clustering.
Edge-Based Segmentation In the phase-contrast image, the gradient image has two kinds of edges: first is between the halos and the background, second is between the halos, and the foreground as shown in Figure 1a. The later has greater value of gradient. Therefore, we infer that halos can be compensated by using a threshold on the gradient. Thus, in the edge-based algorithm, the Sobel approximation of the derivative was used. Initially, the threshold is found automatically by the square root of four times the mean of the gradient image (The MathWorks, I, 2015), which was later tuned, iteratively, to 1.4 for final thresholding. The adjustment factor was required due to the artifact of
Square Euclidean distance was used as measure of distance between the pixels and the means of the clusters. On obser- vation of the PCM image from the clustering perspective, we can see that the bright region is caused by the halos. There is uncertainty about the bright region, whether it is floc or background, due to complex porous structure of flocs. The dark region is certainly either floc or filament. The less dark region is certainly background. Therefore, we considered three clusters initialized at darkest (RGB: 0,0,0), brightest (RGB: 255,255,255), and less dark (RGB: 77,77,77) instances. In the result of k-means clustering, the cluster with less dark centroid is taken as background.
Adaptive Thresholding-Based Segmentation In this approach, we considered three steps with each having
a certain purpose as shown in Figure 5. First, we used average filtering to address shade-off effect. However, it could not eliminate the halos around the borders of the flocs and fila- ments as shown in Figure 6. Finally, we used adaptive thresholding for the segmentation. Precisely, the segmentation method comprises of a
sequence of algorithms as shown in Figure 2. Initially, the RGB image is converted into grayscale image (The Math- Works, I, 2015). The grayscale image was divided by the image obtained by average filtering with a window size of 50×50 pixels. Finally, Bradley adaptive thresholding was used with window size of 101×101 pixels.
Texture-Based Segmentation We observed that range filtering the grayscale image enhances the halo effect associated with PCM. So, we hypothesized that subtraction of the range filtered image from the original grayscale image would improve the seg- mentation accuracy by minimizing the halo effect. Therefore, the algorithm comprises of range filtering over a window of
Figure 4. The artifact of halos in the phase-contrast image of activated sludge.
Figure 5. Flow chart for the proposed adaptive thresholding- based algorithm.
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