F = 12.38161326
P = 2.5459888 X 10^-6
Factor
Df = 3
SS = 73.1152087
MS = 24.3717362
Error
Df = 56
SS = 110.229354
MS = 1.96838132
Sxp = 1.40299014
Tuesday, December 14, 2010
Introduction
Image processing includes a wide range of tactics including edge detection. Among many things, edge detection enables computer to detect shapes and patterns and is used in shape recognition. The human mind is capable of differentiating shapes by drawing inferences about distance, direction, volume, and area consequently allowing humans to be able to “guess” the shape by summarizing the information in which they observe. Computers, on the other hand, have to be programmed to be able to “see” the way a human can. Shape recognition is used for games, biomedical and investigative applications, art and design software, and robotics. It is found on radar systems, surveillance and forensics, and is used to create robots more human-like. (Levine, 1985) Image processing is implemented in machine vision, which is a process by which a computer-driven device optically senses external objects. From the analysis of the sensed data, the device infers information about objects it senses or “sees”. The device is usually a type of camera connected to a computer that digitizes the images and then analyzes them. Machine vision is used for small tasks such as checking size and shape for automobiles, x-rays, photographs, chromosome slides, and cancer smears. ("Machine Vision", 1991)
For this project, an image is imported and processed through a computer. The computer uses image processing, manipulating data in the form of an image, in order for the computer to “read” or interpret the image. An image is usually interpreted as a two-dimensional array of numbers, which resemble the image’s brightness values. Each point, or pixel, has a number according to the color that is shows. A pixel is a number that represents the brightness value of the image at a particular location. (See Appendix) Another important aspect of this project is noise, which is the independent variable. Image noise is the random variation of brightness or color in images creating the image to look fuzzy and grainy. It affects the pattern recognition by making it more difficult for the program to decipher the edges because of the random brightness values. (Sean, 2010) To create noise, a random number is generated from -1 to +1. This generated number is then multiplied by 256, which is the largest color value and represents the blackest black, because the color value should be a double between -256 and +256. This number is then multiplied by the desired percentage change and is added to the original value of the pixel. . (Smith, 2008) For example: if the original color were 100, the generated number came out 0.5293719173, and you wanted to change the pixel by 25%, 33.8798028 would be added to 100 to change the value.
When the image is finished processing, edge detection is used. Edge detection is the process when a computer detects a change in brightness representing the edges in an image or of a particular shape. The edge detection in the experiment uses derivatives to find the edges. A derivative is the slope at a single point. To find all of these, a simple algorithm is written to scan the image horizontal and vertical finding the slope between every point that lay next to each other. To find the efficiency of the algorithm, the signal to noise ratio is calculated. The signal to noise ratio is the contrast between the signal, which is what is being measured without variation, to the undesired signal known as the noise. More noise in the image results in a lower signal to noise ratio, correspondingly, less noise results in a higher signal to noise ratio. (TopBits.com, 2010)
The purpose of this experiment is to find out how random noise in image pixels affects the efficiency of an edge detection algorithm. The independent variable is the noise level on the image; the dependent variable is the efficiency of the algorithm. The efficiency is calculated by the signal to noise ratio. The hypothesis reads that if the amount of noise increases, the efficiency of the algorithm will decrease because it will not be able to detect the shape due to the high and low derivative becoming closer.
Sunday, December 12, 2010
Raw Data
Shape | Trial | %Noise | SNR |
Circle | C | 0 | ∞ |
Circle | 1 | 25 | 4.2578125 |
Circle | 2 | 25 | 5.923913043478260 |
Circle | 3 | 25 | 6.337209302325580 |
Circle | 4 | 25 | 9.39655172413793 |
Circle | 5 | 25 | 5.797872340425530 |
AVERAGE | 6.34267178207346 | ||
Circle | 1 | 50 | 1.8664383561643800 |
Circle | 2 | 50 | 3.40625 |
Circle | 3 | 50 | 3.1142857142857100 |
Circle | 4 | 50 | 2.3491379310344800 |
Circle | 5 | 50 | 2.898936170212770 |
AVERAGE | 2.72700963433947 | ||
Circle | 1 | 75 | 0.9511343804537520 |
Circle | 2 | 75 | 0.8346094946401220 |
Circle | 3 | 75 | 0.9628975265017670 |
Circle | 4 | 75 | 0.8790322580645160 |
Circle | 5 | 75 | 0.8934426229508200 |
AVERAGE | 0.904223256522195 | ||
Circle | 1 | 100 | 0.4972627737226280 |
Circle | 2 | 100 | 0.5444555444555440 |
Circle | 3 | 100 | 0.5126999059266230 |
Circle | 4 | 100 | 0.5079217148182670 |
Circle | 5 | 100 | 0.5816435432230520 |
AVERAGE | 0.528796696429223 |
Shape | Trial | %Noise | SNR |
Square | C | 0 | ∞ |
Square | 1 | 25 | 3.6989247311828000 |
Square | 2 | 25 | 2.6259541984732800 |
Square | 3 | 25 | 2.9783549783549800 |
Square | 4 | 25 | 3.1705069124424000 |
Square | 5 | 25 | 3.323671497584540 |
AVERAGE | 3.1594824636076 | ||
Square | 1 | 50 | 2.8666666666666700 |
Square | 2 | 50 | 2.991304347826090 |
Square | 3 | 50 | 2.8666666666666700 |
Square | 4 | 50 | 3.2 |
Square | 5 | 50 | 3.602094240837700 |
AVERAGE | 3.10534638439943 | ||
Square | 1 | 75 | 2.8786610878661100 |
Square | 2 | 75 | 3.0442477876106200 |
Square | 3 | 75 | 2.5864661654135300 |
Square | 4 | 75 | 2.8907563025210100 |
Square | 5 | 75 | 2.301003344481610 |
AVERAGE | 2.74022693757858 | ||
Square | 1 | 100 | 1.0766823161189400 |
Square | 2 | 100 | 1.2531876138433500 |
Square | 3 | 100 | 1.1505016722408000 |
Square | 4 | 100 | 0.9234899328859060 |
Square | 5 | 100 | 0.9424657534246580 |
AVERAGE | 1.06926545770273 |
Shape | Trial | %Noise | SNR |
Triangle | C | 0 | ∞ |
Triangle | 1 | 25 | 1.6015831134564600 |
Triangle | 2 | 25 | 1.5524296675191800 |
Triangle | 3 | 25 | 1.5251256281407000 |
Triangle | 4 | 25 | 1.4050925925925900 |
Triangle | 5 | 25 | 1.3733031674208100 |
AVERAGE | 1.49150683382595 | ||
Triangle | 1 | 50 | 0.6692392502756340 |
Triangle | 2 | 50 | 0.7082847141190200 |
Triangle | 3 | 50 | 0.7183431952662720 |
Triangle | 4 | 50 | 0.640295358649789 |
Triangle | 5 | 50 | 0.7149587750294460 |
AVERAGE | 0.690224258668032 | ||
Triangle | 1 | 75 | 0.4967266775777410 |
Triangle | 2 | 75 | 0.4963205233033520 |
Triangle | 3 | 75 | 0.6112789526686810 |
Triangle | 4 | 75 | 0.5409982174688060 |
Triangle | 5 | 75 | 0.48951612903225800 |
AVERAGE | 0.526968100010168 | ||
Triangle | 1 | 100 | 0.40066006600660100 |
Triangle | 2 | 100 | 0.41746905089408500 |
Triangle | 3 | 100 | 0.4118046132971510 |
Triangle | 4 | 100 | 0.40683646112600500 |
Triangle | 5 | 100 | 0.39986824769433500 |
AVERAGE | 0.407327687803635 |
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