Hsu - Revision history

imported>Projects221: /* CFA Interpolation */

2013-03-21T06:45:11Z

CFA Interpolation

← Older revision		Revision as of 06:45, 21 March 2013
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	While images files are usually represented in three color channels, digital cameras typically only have one image sensor. For the sensor to capture three different light wavelengths, a color filter array (CFA) is placed in front of the image sensor so that each pixel is only allowed to capture a narrow spectrum of light. The most common type of CFA is the Bayer filter (shown in the figure on the right), which is divided between red, green, and blue light. The Bayer filter uses 50% green pixels since the human eye is more sensitive to green light. This work assumes that all test images employ the Bayer filter. [[File:Bayer.gif\|thumb\|Bayer filter array. (www.analog.com)]]		While images files are usually represented in three color channels, digital cameras typically only have one image sensor. For the sensor to capture three different light wavelengths, a color filter array (CFA) is placed in front of the image sensor so that each pixel is only allowed to capture a narrow spectrum of light. The most common type of CFA is the Bayer filter (shown in the figure on the right), which is divided between red, green, and blue light. The Bayer filter uses 50% green pixels since the human eye is more sensitive to green light. This work assumes that all test images employ the Bayer filter. [[File:Bayer.gif\|thumb\|Bayer filter array. (www.analog.com)]]

	=== CFA Interpolation ===		=== CFA Interpolation [1] ===
	After the image is captured by the sensor on the Bayer array, the channels are interpolated into a full three-channel color image.		After the image is captured by the sensor on the Bayer array, the channels are interpolated into a full three-channel color image.

imported>Projects221: /* Smooth Hue */

2013-03-21T06:44:46Z

Smooth Hue

← Older revision		Revision as of 06:44, 21 March 2013
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	==== Smooth Hue ====		==== Smooth Hue ====
	A smooth hue filter averages hue ~~to interpolate images. Hue is~~ the ratio between ~~the~~ red/blue ~~channels~~ and the green ~~channel~~, and ~~missing pixels are bilinearly interpolated according to~~ hue.		A smooth hue filter averages hue, the ratio between a chrominance channels (red or blue) and the luminance channel (green), to interpolate pixels. This method uses pixels from 2 color channels and assumes that hue does not change significantly over a small area.

	== Tamper Detection ==		== Tamper Detection ==

imported>Projects221: /* Code */

2013-03-21T06:37:39Z

Code

← Older revision		Revision as of 06:37, 21 March 2013
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	==Code==		==Code==
	[[File:~~CodeFile~~.zip]]		[[File:Hsu.zip]]

	==Data==		==Data==
	Images used for testing were provided by the class.		Images used for testing were provided by the class.

imported>Projects221: /* Measure of Similarity */

2013-03-21T06:34:08Z

Measure of Similarity

← Older revision		Revision as of 06:34, 21 March 2013
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	<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>		<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>

	where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure on the left shows the ideal Fourier transform for the green channel while the figure on the right shows the measures of similarity for a real and ~~untampered~~ image. The tampered region can be clearly seen to be in Block 2.		where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure on the left shows the ideal Fourier transform for the green channel while the figure on the right shows the measures of similarity for a real and tampered image. The tampered region can be clearly seen to be in Block 2.

	[[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and ~~untampered~~ image.]]		[[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and tampered image.]]

	=== Windowing ===		=== Windowing ===

imported>Projects221: /* References - Resources and related work */

2013-03-21T06:32:49Z

References - Resources and related work

← Older revision		Revision as of 06:32, 21 March 2013
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	[2] Dirik, A.E.; Memon, N., "Image tamper detection based on demosaicing artifacts," Image Processing (ICIP), 2009 16th IEEE International Conference on , vol., no., pp.1497,1500, 7-10 Nov. 2009.		[2] Dirik, A.E.; Memon, N., "Image tamper detection based on demosaicing artifacts," Image Processing (ICIP), 2009 16th IEEE International Conference on , vol., no., pp.1497,1500, 7-10 Nov. 2009.

			[3] http://en.wikipedia.org/wiki/Bicubic_interpolation

	= Appendix I - Code and Data =		= Appendix I - Code and Data =

imported>Projects221: /* Linear and Single Channel */

2013-03-21T06:32:26Z

Linear and Single Channel

← Older revision		Revision as of 06:32, 21 March 2013
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	<li>Bilinear: Biinear filters interpolate by taking the linear average of neighboring pixels. For the green channel, this is represented as		<li>Bilinear: Biinear filters interpolate by taking the linear average of neighboring pixels. For the green channel, this is represented as
	<math>\begin{bmatrix}0 & \frac{1}{4} & 0 \\\frac{1}{4} & 0 & \frac{1}{4} \\ 0 & \frac{1}{4} & 0 \end{bmatrix} </math> where each interpolated pixel is the average of its neighboring pixels </li>		<math>\begin{bmatrix}0 & \frac{1}{4} & 0 \\\frac{1}{4} & 0 & \frac{1}{4} \\ 0 & \frac{1}{4} & 0 \end{bmatrix} </math> where each interpolated pixel is the average of its neighboring pixels </li>
	<li>Bicubic: Bicubic filters are similar to bilinear filters but require an 8x8 filter to calculate the weighted average of 16 pixels.		<li>Bicubic: Bicubic filters are similar to bilinear filters but require an 8x8 filter to calculate the weighted average of 16 pixels. Bicubic filters typically achieve higher smoothness than bilinear filters due to the larger filter but are slower to calculate [3].
	</li>		</li>
	</ol>		</ol>

imported>Projects221: /* Measure of Similarity */

2013-03-21T06:25:34Z

Measure of Similarity

← Older revision		Revision as of 06:25, 21 March 2013
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	<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>		<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>

	where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure on the left shows the ideal Fourier transform for the green channel while the figure on the right shows the measures of similarity for a real and untampered image. The tampered region can be clearly seen to be in Block 2.		where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure on the left shows the ideal Fourier transform for the green channel while the figure on the right shows the measures of similarity for a real and untampered image. The tampered region can be clearly seen to be in Block 2.

	[[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and untampered image.]]		[[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and untampered image.]]

imported>Projects221: /* Measure of Similarity */

2013-03-21T06:25:00Z

Measure of Similarity

← Older revision		Revision as of 06:25, 21 March 2013
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	<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>		<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>

	where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure ~~below~~ on the right shows the measures of similarity for a real and untampered image. The tampered region can be clearly seen to be in ~~Block2~~. [[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and untampered image.]]		where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure on the left shows the ideal Fourier transform for the green channel while the figure on the right shows the measures of similarity for a real and untampered image. The tampered region can be clearly seen to be in Block 2.
			[[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and untampered image.]]

	=== Windowing ===		=== Windowing ===

imported>Projects221: /* Measure of Similarity */

2013-03-21T06:22:21Z

Measure of Similarity

← Older revision		Revision as of 06:22, 21 March 2013
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	<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>		<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>

	where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ~~[[File:FFTideal.png\|thumb\|Ideal FFT of green channel.]]~~ ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure below shows the measures of similarity for a real and untampered image. [[File:realtamper.png]]		where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure below on the right shows the measures of similarity for a real and untampered image. The tampered region can be clearly seen to be in Block2. [[File:FFTideal.png\|400px\|Ideal FFT of green channel.]] [[File:realtamper.png\|400px\|Measures of similarity for a real and untampered image.]]

	=== Windowing ===		=== Windowing ===

imported>Projects221: /* Measure of Similarity */

2013-03-21T06:19:29Z

Measure of Similarity

← Older revision		Revision as of 06:19, 21 March 2013
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	<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>		<math> M(p, s) = \sum\limits_{w_{x}, w_{y}} {P \times S}</math>

	where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. [[File:FFTideal.png\|thumb\|Ideal FFT of green channel.]] ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image.		where ''P'' is the Fourier transform of the calculated probability map and ''S'' is the Fourier transform of the ideal probability map for each channel. The similarity between the ideal and calculated probability maps determines whether or not the image has been modified; high similarity indicates that the given CFA interpolation of the image can be approximated using a linear array since the frequency content of the probability map will be close to ideal. In contrast, tampering changes the frequency content of the probability map and the frequencies between the ideal and real case will result in a lower similarity measure. [[File:FFTideal.png\|thumb\|Ideal FFT of green channel.]] ''P'' was not normalized since the algorithm compares the frequency content between blocks of the image. The figure below shows the measures of similarity for a real and untampered image. [[File:realtamper.png]]

	=== Windowing ===		=== Windowing ===