## 3 Results
(We chose asymmetric kernels with even edge lengths instead of the more commonly used symmetric kernels with odd edge lengths as they yielded more accurate results. This could be because asymmetric kernels did not completely cancel out the effects of erosion and dilation.) Contours with areas smaller than \(1/8\)th of the largest contour area in any image sequence were ignored for the cells, whereas contours with areas smaller than \(1/20\)th of the largest contour area were discarded for the uncategorized boundary objects. The overall processing time for an image was 0.88 s on an average with a standard deviation of 0.08 s, barring the smudge removal step that needed to be computed once and took about 25.5 s.  
The CNN was trained on the 2000 sub images that were evenly split between the positive and negative samples. This even split ensured there was no bias towards predicting one kind of sample over the other to improve modeling accuracy. The training occurred over 500 epochs or iterations, where, in each epoch, the 2000 sub images were randomly split into training and testing sets following an 80:20 ratio. The CNN was learned using the training set of that epoch, after which the trained CNN was evaluated on the testing set of that epoch. Such repeated training and testing prevented over fitting of the CNN to any particular type of the images. A weighted average form of the individual CNNs learned during each epoch was considered as the final model so as to minimize the prediction error over all the training samples. It took about seven hours to complete the training process. We then used the learned CNN to process completely new test images comprising one or more clusters of silica beads in less than a second. Representative examples of a few such processed images are shown in Figure 19. Note that the CNN performs well in terms of detecting all the individual beads as long as they are of similar sizes, i.e., present at similar \(z\)-planes. Figure 18: Examples of negative training samples for the convolutional neural network. We compared our method with four other methods that have some variations in one or more of our object perception steps. The first and last of these comparison methods use maximally stable extremal regions [49], or MSER in short, for bead detection. All the other steps remain the same as in our method. MSER detects regions of interest based on their intensity functions and, thus, provides certain useful characteristics such as stability and invariance to affine transformations for the detected regions. MSER requires several parameters, namely, variation, minimum area, maximum area, maximum variation, and minimum diversity. We selected 13.5, 4000, 6000, 0, and 0 as the parameter values for the dicy cells, 13.5, 500, 775, 0, and 0 for the HUVECs, and 4, 100, 700, 0, and 0 for the clustered beads. Our first comparison method uses an additional circularity parameter that is given by the absolute difference in blob radius between the \(x\)- and \(y\)-directions. This parameter was always selected to be 3. The second perception method uses speeded up robust features, or SURF in short [50], for bead detection. Again, none of the other steps changes from our method. SURF uses a Haar wavelet based feature descriptor that computes an integer approximation of the determinant of the Hessian matrix for the pixel intensities in the blobs of interest. We chose a threshold Hessian value of 1800, four octaves and three octave layers for the dicy cells, 30,000, four and three for the corresponding parameters in the case of the HUVECs, and 26,000, four and three as the parameters for the clustered beads. The third comparison method uses [PERSON]'s thresholding technique for Canny edge detection, keeping all the other steps the same as that of our method, to automatically segment an image into a background class and a foreground class that minimizes the weighted within-class variance [51].