Set of Images - Lab Report Example

 Exercise 1.1. Moving average smoothers. Images can be smoothed to soften edges or compensate for random noise in an image using IDL’s SMOOTH function. SMOOTH performs an equally weighted smoothing using a square neighborhood of an arbitrary odd width. The command EDGE_TRUNCATE was set to apply the smoothing function to all points. PHOTO PHOTO PHOTO PHOTO PHOTO original noise 5 span Figure 1 13 span 20 span PHOTO PHOTO PHOTO PHOTO PHOTO original noise 5 span 13 span 20 span Figure 1.1 Average smoothing with edge truncate. Noise was applied to an image of a fork. The application of the moving average filter was then used. The fork image with (5 span) (figure 1)showed a reduction in noise. Increasing the span decreased the noise, but on these images, fine details become lost. The greater the span and the smoother the image, the less detail that is shown in the image. The second set of images showed the same trend as the first. An original image with noise added can be smoothed through the moving average filter and the noise reduced. As in the first set of images, the greater the span, the smoother the image, but there is also a greater of loss of detail. With this increased span, the (20 span) image (figure 1.1) was almost indistinguishable from the original image. Exercise 1.2. When the keyword EDGE_TRUNCATE is used with the SMOOTH command, the smoothing function is applied to all points. There is no smoothing if the end points are not copied. PHOTO PHOTO Figure 1.2 Two orders of moving average smoothers were explored. The images generated had a narrow band of noise around them. As the span value increased (figure 1.2) the image became less distinct. Exercise 1.3. Effect on moving average smoothers with and without EDGE_TRUNCATE. A variety of moving average smoothers were applied to an image with and without the EDGE_TRUNCATE keyword used. Without EDGE_TRUNCATE PHOTO PHOTO PHOTO PHOTO original noisy 15 span 40 span With EDGE_TRUNCATE PHOTO PHOTO PHOTO PHOTO original noisy 15 span 40 span Figure 1.3 Average smoothing without/with EDGE_TRUNCATE. When EDGE_TRUNCATE is applied to a noisy image using the moving average filter, the noise in the image decreases. However, as the span is increased, the image becomes smoother and loses definition. Without EDGE_TRUNCATE, a narrow band of noise remains around the image, this band increases as the span increases. The middle of this image has less definition than the image with EDGE_TRUNCATE. Exercise 2.1. Moving average filter compared to median filter. Median filtering is effective in removing salt and pepper noise (isolated high or low values). The resulting image has a less grainy appearance than the original. 2.1= strength=3000 average filter(span=5) with the median filter( med_width=5) PHOTO PHOTO PHOTO PHOTO original noisy Figure 2.1 moving average filter median filter An original image had noise applied to it. The noisy image was then manipulated by applying the moving average filter with 5 span and median filter with med width 5 with shot strength 3000 to the image. The image that resulted had the noise reduced, but the image was blurry, it was smoother than the noisy image and had lost a great deal of detail. When the noisy image had the median filter applied to it, there was a narrow band around the image edge that retained the noise, but the objects in the image had no noise. The image that resulted using the median filter (figure 2.1) was smoother, with indistinguishable noise, and there was a sharper edge on the objects in the image than the moving average filter image. Exercise 2.2. Median and moving average filters adjusted. shot strength=30000 average filter(span=5) with the median filter( med_width=5) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure 2.2A strength=30000 average filter(span=10) with the median filter( med_width=10) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure2.2B strength=30000 average filter(span=15) with the median filter( med_width=15) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure2.2C A shot strength of 3000 was used on an image, noise was added. The image was examined using the average filter with a span of 5. This image showed a minor reduction in noise and smoother objects. The median filter image was then compared to the moving average filter image. The objects in this image were sharper and more distinguishable (figure 2.2A), the noise in the image was less The shot strength was increased to 30000 and an image had noise added to compare the moving average filter with the median filter (figure 2.2B). The moving average filter produced an image that still had noise and the detail in the objects in the image were lost. The application of a median filter reduced the noise more than the moving average and the objects in the image were sharper, more defined. Noise was reduced when the image had an application of 15 span with moving average and the same value of width with median filter(figure 2.2C). There was less detail than the image in (figure 2.2B). The moving average filter provided little noise and a smooth image, but the image is blurred and loses detail. The median filter provides sharp images, sharp edges, but the details in the image’s objects are lost. Additionally, the edges in the median filter image are unsmoothed when compared with moving average images. The images for the moving average show that the greater the span, the less the noise, but, also, less detail in the image’s objects. Noise in the images with median filter were retained in a narrow band around the image, but noise inside of the image was reduced as the span increased. The median filter images retained more of a sharpness with less smoothing than the moving average images. Exercise 2.3. Pixel noise threshold. PHOTO PHOTO Shot noise= 45000 moving average shot noise= 45000 median filter Figure 2.3 Shot noise of 45000 was applied to an image using both the moving average and the median filter. There is a threshold where the median filter is ineffective. The image using the moving average was identifiable and the median filter image was pixilated. Exercise 2.4. Adjusting shot strength variable and the median and moving average filter. Strength=30000 average filter(span= 5) with the median filter( med_width= 5) PHOTO PHOTO PHOTO PHOTO original Noisy moving median filter Figure 2.4A strength=30000 average filter(span=10) with the median filter( med_width=10) PHOTO PHOTO PHOTO PHOTO original noisy moving median filter Figure 2.4 B strength=30000 average filter(span=15) with the median filter( med_width=15) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure 2.4 C Strength=30000 average filter(span=5) with the median filter( med_width=5) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure 2.4 D Strength=30000 average filter(span=10) with the median filter( med_width=10) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure 2.4 E Strength=30000 average filter(span=15) with the median filter( med_width=15) PHOTO PHOTO PHOTO PHOTO original noisy moving average median filter Figure 2.4 F Images manipulated with the moving average filter show that the greater the span the more distinguishable the image is. The same is shown by the images generated using the median filter. The images using the median filter also show that the greater the span the more sharper the image. While the median filter images are sharper, compared to moving average images with the same span/width, the moving average images retain more of the original image’s detail. Exercise 3.1 Gaussian kernel compared to moving average filter Filtering is a common image and signal processing technique.  It can be used to smooth, sharpen, de-blur, and restore images. The Gaussian kernel provides a form of low pass filtering that preserves the low frequency components of an image. Convolving with User defined Kernels( 5x5) PHOTO PHOTO PHOTO PHOTO original noisy moving average(5) kernel A noisy image that has the kernel filter applied to it is brighter than an image created using the moving average. It is more like the original image. The kernel filter creates a form around an image and this image is smoother and less grainy than the moving average image. Conclusion: Images which are provided by moving average appeared smoother and contained more detail than the median filter. Median filter provides a sharp image with less noise, but the image loses detail. Read More