12th Activity: Video Processing

     The aim of this activity is to measure physical quantities using video processing. Image processing learned from previous activities can be utilized on image frames of a video. A camera was used to capture a video showing a kinematic phenomenon. We chose to observe a pendulum and obtain the acceleration due to gravity. 

      For segmentation, the RGB layers for a single frame were observed. It was shown in Figure 1. It can be seen that the bob of the pendulum is more prominent in the green layer. Thus, it can be set to a threshold value to isolate the bob of the pendulum. 

Figure 1. RGB layers of a single frame

     The threshold value that was used was 0.5. Figure 2 shows the segmented image of five consecutive frames. Differences between consecutive frames are not very evident since there is 24.39 frames per second. 

Figure 2. Segmented images of five consecutive frames

     

     The method for obtaining the period and the acceleration due to gravity was quite unique. One way is to obtain the center of mass of the bob of the pendulum. However, an easier way is to observe the overlapping of consecutive frames.  The basic theory in a pendulum was utilized here. As the bob of the pendulum reaches the point of minimum kinetic energy, the distance travelled at a certain time decreases. Since the time interval between each frame is constant, the overlap between two consecutive frames increase. On the other hand, as the bob reaches the point wherein the kinetic energy is at its maximum the distance that the bob has move increases. Thus, the overlap between two consecutive frames is then smaller. 

     To know the number of pixels that overlaps between consecutive frames, the images were first multiplied. Then the sum of the matrix of their product was obtained. This was done for 100 frames. Figure 3 shows the plot of the number of overlapping pixels vs. frame. It can be seen that there are several peaks. 

Figure 3. Number of overlapping pixels

     These peaks suggests the relative time at which the bob of the pendulum reaches minimum kinetic energy. Therefore, alternating peaks constitute for the period of the pendulum. Since there are 24.39 frames per second, the period of the pendulum is 1/24.39 which is equal to 0.0410004 sec. 

    Given the period and the length of the string, the acceleration due to gravity can then be calculated. Note that the length of the string is 30cm. From Figure 3, there are 26 frames that will complete a period. The acceleration due to gravity is given by

 
     Inserting all the obtained value for each parameters, the equation becomes

     The calculated acceleration due to gravity was found to be 10.409776m/sec. The analytical value for the acceleration due to gravity is 9.81m/sec. The percent error is then 

     The obtained percent error is relatively low. Thus, the use of image processing on series  of images to calculate physical quantities are also efficient. 

Reference

[1] Soriano, M. A12 - Video Processing. 2012



Self - evaluation

I will give myself a grade of 11 for producing the output in a more intuitive and a much easier manner. The calculated physical quantity was indeed near the accepted value. Also, ideas from previous activities were utilized. 

11th Activity: Color Image Segmentation

     Previously, regions of interest were isolated from their background. This is done to do more analysis and processing. Thresholding were done previously but this time, color will be used to segment images since thresholding won't be useful when grayscale value of the region of interest is the same as that of the background. 

     This activity will implement parametric and non-parametric probability distribution to segment images based on color. 

  

     For every pixel, there is a corresponding red, green, and blue values. The normalized chromaticity coordinates is given by

where I = R + G + B and r+g+b=1. Since b=1-r-g, the chromaticity can be explained by r and g. Figure 1 shows the normalized chromaticity space. 

Figure 1. The normalized chromaticity space

      An image of an object with a blue color was obtained as shown in Figure 2.  The blue box will then be segmented using the parametric and non-parametric probability distribution.  A monochromatic region was cropped from the region of interest. It is also shown in Figure 2. 

     

Figure 2. Image to be used for segmentation (left) ; patch from the image (right)

     The color of the patch was represented as points in the NCC space. Since the object is mainly blue, the coordinates must lie in the blue region in the NCC space. 

     After cropping a monochromatic part of the region of interest, the histogram of it was calculated. An algorithm was done in Scilab to derive the Gaussian Probability Distribution Function. The mean (μ_r and μ_g) and standard deviation (σ_r and σ_g) were first calculated. Then the probability can be obtained separately  by  

     This is then the probability that a certain pixel belongs to the region of interest. The joint probability is obtained by multiplying the probability that a pixel with chromaticity r to the probabilty that a pixel with chromaticity g belong to the ROI. 

     Figure 3 shows the resulting image after applying the Gaussian Probability Distribution Function. It can be seen that the

Figure 3. Output from parametric segmentation

        For the non-parametric probability distribution estimation, the location of the rg chromaticity was first taken and it is shown in Figure 4. The 2D histogram of the region of interest was obtained using the code provided in the manual: 

   

Figure 4. 2D histogram

     Figure 5 shows the resulting segmented image after histogram backprojection. The 2D histogram that was obtained previously was used to backproject the image to be segmented. 

Figure 5. Output from non-parametric segmentation

     It can be observed from the two methods were able to isolate the region of interest from its background. However, in the parametric segmentation the shading variations were more captured compared with the output from the non-parametric probability distribution estimation. The advantage of the non-parametric probability distribution estimation is that the use of histogram backprojection makes it a much easier method. 

     

Reference

[1] Soriano, M. A11 - Image Color Segmentation. 2010

Self-evaluation:

I would give myself a 10 for producing all the necessary output. I was also able to learn and understand the ideas behind the activity. 

Activity 10: Applications of Morphological Operations 3 of 3: Looping through Images

The final activity for the applications of morphological operations is about differentiating shapes with varying sizes in a given image. We will try to isolate the desired regions of interest from background noises.

Figure 1 is an image of circles which are actually punched papers. The whole image was divided into 99 sub-images with a size of 256x256 pixel. This was done automatically and randomly using Scilab.

Figure 1. Image of punched papers

     Figure 2 shows the sub-images. A sub-image was then opened and its histogram was also obtained to know the threshold value. It was found to be 0.8. Using this value, the sub-images were converted into binary sub-images as shown at the right in Figure 2.

Figure 2. Sub-images with 256x256 pixel each and their corresponding binarized sub-images

    The morphological operations such as open and close were used to clean the image. These are not readily available in SIP toolbox. However, these operations can be defined in terms of dilation and erosion operators. 

     Opening operator is the dilation of the eroded image with a same structuring element. It is given by 

where A is the image and B is the structuring element. 

     On the other hand, closing operator is the erosion of the dilated image. It is given by 

     Figure 3 shows the opening and closing of two sub-images. Indeed, the images were cleaned after applying opening and closing operations.

Figure 3. 1st column: original sub-images, 2nd column: Opening operator were applied; 3rd column: Closing operator were applied

      bwlabel  function was used to label each circle. The area of each circle for each sub-image was then calculated. Figure 4 shows the histogram of the area. It can be seen from the histogram that most of the blobs have an area from 450 to 600 pixels.

Figure 4. Histogram of area of blobs

       To obtain the best estimate, the area between the range of 450 to 600 pixels were averaged. Also the standard deviation was obtained. Thus, the area of the blob is 518.25±25.90 pixels. 

     The next task is to isolate the bigger cells shown in Figure 5. It was first turned to binary image with a threshold value of 0.8. 

Figure 5. Image of circles with enlarged circles

     A structuring element was created using a circle with a radius of 15pixels. The radius was such since we need to create a structuring element with an area slightly greater than the obtained area previously. Using morphological operations again, the bigger cells were then isolated from the background noise. Opening operator was used after it was eroded. The resulting image is shown in Figure 6.

Figure 6. Isolated enlarged blobs

References:

[1] Soriano, M. 2012. A10 Applications of Morphological Operations 3 of 3: Looping through Images

[2]en.wikipedia.org/wiki/Opening_(morphology)

[3]en.wikipedia.org/wiki/Closing_(morphology) 

Self-evaluation 

I would give myself a 10 since I was able to produce the necessary output and was able to explain my thoughts clearly. It was a very fun activity. :)