BoinJou - Revision history

imported>Projects221: /* Assumptions */

2013-03-21T07:52:02Z

Assumptions

← Older revision		Revision as of 07:52, 21 March 2013
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	3. Tampered zone is not too big.		3. Tampered zone is not too big.

	For our subsequent classification section, we assume that the tampered zone occupies less than ~~60%~~ of the test image. This assumption is made because even if the tampered zone is larger than this assumed size, our clustering algorithm should still be able to cluster into 2 distinct regions. In other words, it's just a matter of switching of perspective: which is tampered and which is not, and which cluster is larger, and which is smaller.		For our subsequent classification section, we assume that the tampered zone occupies less than a certain fraction of the test image (usually around 50%). This assumption is made because even if the tampered zone is larger than this assumed size, our clustering algorithm should still be able to cluster into 2 distinct regions. In other words, it's just a matter of switching of perspective: which is tampered and which is not, and which cluster is larger, and which is smaller.

	== Classification ==		== Classification ==

imported>Projects221: /* Assumptions */

2013-03-21T07:51:05Z

Assumptions

← Older revision		Revision as of 07:51, 21 March 2013
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	2. Tampered zone is not too small.		2. Tampered zone is not too small.

	We make this assumption because small tampered zones are hard to visually detect in the first place, so this is a hard problem by itself. We run our algorithm with 64x64 pixel sliding blocks, and if the tampered region is contained inside these blocks, it might not be detected.		We make this assumption because small tampered zones are hard to visually detect in the first place, so this is a hard problem by itself. We run our algorithm with 64x64 pixel sliding blocks, and if the tampered region is contained inside these blocks, it might not be detected. This will be discussed in a more detailed way in the "Analysis and ideas for improvement" section.

	3. Tampered zone is not too big.		3. Tampered zone is not too big.

imported>Projects221: /* Clustering Algorithm */

2013-03-21T07:49:03Z

Clustering Algorithm

← Older revision		Revision as of 07:49, 21 March 2013
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	We realized, from the FFT peak maps as mentioned before, that just using the minimum of that map already localizes the tampered region pretty well, though very roughly. Therefore, for initialization, we choose the centroid of the smaller cluster to be the block with the minimum FFT peak value. We then randomly generate the initial centroid for the other cluster until we have a centroid position that is at least half the image size away. This is done to reduce the chances of picking the second centroid in the tampered region as well.		We realized, from the FFT peak maps as mentioned before, that just using the minimum of that map already localizes the tampered region pretty well, though very roughly. Therefore, for initialization, we choose the centroid of the smaller cluster to be the block with the minimum FFT peak value. We then randomly generate the initial centroid for the other cluster until we have a centroid position that is at least half the image size away. This is done to reduce the chances of picking the second centroid in the tampered region as well.

	Lastly, we run this clustering algorithm with different weightings between the FFT peak portion of the 27-dimensional vector and the <math>\overrightarrow{\alpha}</math> portion of the vector. We do this because some images are classified more easily by the ~~FFt~~ peak while others are clustered more easily with the <math>\overrightarrow{\alpha}</math>. For example, if the image was not taken from a camera with a Bayer pattern CFA, then the intensities of the FFT peak would not give us much information, since the peak of the Fourier Transform would be somewhere else. In that case we would rely more on using the <math>\overrightarrow{\alpha}</math> to cluster. Below we show an example of 5 different weightings and the different clustering maps we obtain from them. We can see visually that there is an optimum for a certain weighting (red box).		Lastly, we run this clustering algorithm with different weightings between the FFT peak portion of the 27-dimensional vector and the <math>\overrightarrow{\alpha}</math> portion of the vector. We do this because some images are classified more easily by the FFT peak while others are clustered more easily with the <math>\overrightarrow{\alpha}</math>. For example, if the image was not taken from a camera with a Bayer pattern CFA, then the intensities of the FFT peak would not give us much information, since the peak of the Fourier Transform would be somewhere else. In that case we would rely more on using the <math>\overrightarrow{\alpha}</math> to cluster. Below we show an example of 5 different weightings and the different clustering maps we obtain from them. We can see visually that there is an optimum for a certain weighting (red box).
	[[File:weighting.png\|600px\|center\|thumb\|Figure 6: Five clustering results using different weightings between the alpha vector and the FFT peaks. The optimum weighting is show in the red box.]]		[[File:weighting.png\|600px\|center\|thumb\|Figure 6: Five clustering results using different weightings between the alpha vector and the FFT peaks. The optimum weighting is show in the red box.]]

imported>Projects221: /* Clustering Algorithm */

2013-03-21T07:43:43Z

Clustering Algorithm

← Older revision		Revision as of 07:43, 21 March 2013
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	Lastly, we run this clustering algorithm with different weightings between the FFT peak portion of the 27-dimensional vector and the <math>\overrightarrow{\alpha}</math> portion of the vector. We do this because some images are classified more easily by the FFt peak while others are clustered more easily with the <math>\overrightarrow{\alpha}</math>. For example, if the image was not taken from a camera with a Bayer pattern CFA, then the intensities of the FFT peak would not give us much information, since the peak of the Fourier Transform would be somewhere else. In that case we would rely more on using the <math>\overrightarrow{\alpha}</math> to cluster. Below we show an example of 5 different weightings and the different clustering maps we obtain from them. We can see visually that there is an optimum for a certain weighting (red box).		Lastly, we run this clustering algorithm with different weightings between the FFT peak portion of the 27-dimensional vector and the <math>\overrightarrow{\alpha}</math> portion of the vector. We do this because some images are classified more easily by the FFt peak while others are clustered more easily with the <math>\overrightarrow{\alpha}</math>. For example, if the image was not taken from a camera with a Bayer pattern CFA, then the intensities of the FFT peak would not give us much information, since the peak of the Fourier Transform would be somewhere else. In that case we would rely more on using the <math>\overrightarrow{\alpha}</math> to cluster. Below we show an example of 5 different weightings and the different clustering maps we obtain from them. We can see visually that there is an optimum for a certain weighting (red box).
	[[File:weighting.png\|600px\|center\|thumb\|Figure 6: Five clustering results using different weightings between the alpha vector and the FFT peaks.]]		[[File:weighting.png\|600px\|center\|thumb\|Figure 6: Five clustering results using different weightings between the alpha vector and the FFT peaks. The optimum weighting is show in the red box.]]

	==Assumptions==		==Assumptions==

imported>Projects221: /* Clustering Algorithm */

2013-03-21T07:43:16Z

Clustering Algorithm

← Older revision		Revision as of 07:43, 21 March 2013
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	Lastly, we run this clustering algorithm with different weightings between the FFT peak portion of the 27-dimensional vector and the <math>\overrightarrow{\alpha}</math> portion of the vector. We do this because some images are classified more easily by the FFt peak while others are clustered more easily with the <math>\overrightarrow{\alpha}</math>. For example, if the image was not taken from a camera with a Bayer pattern CFA, then the intensities of the FFT peak would not give us much information, since the peak of the Fourier Transform would be somewhere else. In that case we would rely more on using the <math>\overrightarrow{\alpha}</math> to cluster. Below we show an example of 5 different weightings and the different clustering maps we obtain from them. We can see visually that there is an optimum for a certain weighting (red box).		Lastly, we run this clustering algorithm with different weightings between the FFT peak portion of the 27-dimensional vector and the <math>\overrightarrow{\alpha}</math> portion of the vector. We do this because some images are classified more easily by the FFt peak while others are clustered more easily with the <math>\overrightarrow{\alpha}</math>. For example, if the image was not taken from a camera with a Bayer pattern CFA, then the intensities of the FFT peak would not give us much information, since the peak of the Fourier Transform would be somewhere else. In that case we would rely more on using the <math>\overrightarrow{\alpha}</math> to cluster. Below we show an example of 5 different weightings and the different clustering maps we obtain from them. We can see visually that there is an optimum for a certain weighting (red box).
	[[File:weighting.png\|600px\|center]]		[[File:weighting.png\|600px\|center\|thumb\|Figure 6: Five clustering results using different weightings between the alpha vector and the FFT peaks.]]

	==Assumptions==		==Assumptions==

imported>Projects221: /* Alpha vectors */

2013-03-21T07:41:14Z

Alpha vectors

← Older revision		Revision as of 07:41, 21 March 2013
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	Here we are still using the same example difference image as shown above in Figure 3, where the tampered region is shown, highlighted in the yellow box.		Here we are still using the same example difference image as shown above in Figure 3, where the tampered region is shown, highlighted in the yellow box.
	Below we have shown the map of the computed norms for this image, and we can see that the high value regions correspond well to the tampered region in the difference image.		Below we have shown the map of the computed norms for this image, and we can see that the high value regions correspond well to the tampered region in the difference image.
	[[File:alpha_maxs.png\|650px\|center\|thumb\|Figure 6: Alpha vector norm map of the tampered image. High valued blocks correspond nicely to tampered regions.]]		[[File:alpha_maxs.png\|650px\|center\|thumb\|Figure 5: Alpha vector norm map of the tampered image. High valued blocks correspond nicely to tampered regions.]]

	===Clustering Algorithm===		===Clustering Algorithm===

imported>Projects221: /* Alpha vectors */

2013-03-21T07:40:59Z

Alpha vectors

← Older revision		Revision as of 07:40, 21 March 2013
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	===Alpha vectors===		===Alpha vectors===
	For our EM algorithm, we set the neighborhood of interpolation to be 1, so we get 8 <math>\alpha</math> coefficients that make up an <math>\overrightarrow{\alpha}</math> for each block in every color channel. What we did is find the median <math>\overrightarrow{\alpha}</math> of the image, and compute the norm of every <math>\overrightarrow{\alpha}</math> associated with every block with this median value. The idea behind this is that for tampered regions, the resulting norm values would be large, since the tampered regions would have the most different <math>\overrightarrow{\alpha}</math> values compared to the rest of the image.		For our EM algorithm, we set the neighborhood of interpolation to be 1, so we get 8 <math>\alpha</math> coefficients that make up an <math>\overrightarrow{\alpha}</math> for each block in every color channel. What we did is find the median <math>\overrightarrow{\alpha}</math> of the image, and compute the norm of every <math>\overrightarrow{\alpha}</math> associated with every block with this median value. The idea behind this is that for tampered regions, the resulting norm values would be large, since the tampered regions would have the most different <math>\overrightarrow{\alpha}</math> values compared to the rest of the image.
	Here is the same example difference image as shown above, where the tampered region is shown, highlighted in the yellow box.		Here we are still using the same example difference image as shown above in Figure 3, where the tampered region is shown, highlighted in the yellow box.
	~~[[File:diff_nc.png\|350px\|center\|thumb\|Figure 5: Example difference image between real and tampered version. The tampered region is show in the yellow box.]]<br>~~
	Below we have shown the map of the computed norms for this image, and we can see that the high value regions correspond well to the tampered region in the difference image.		Below we have shown the map of the computed norms for this image, and we can see that the high value regions correspond well to the tampered region in the difference image.
	[[File:alpha_maxs.png\|650px\|center\|thumb\|Figure 6: Alpha vector norm map of the tampered image. High valued blocks correspond nicely to tampered regions.]]		[[File:alpha_maxs.png\|650px\|center\|thumb\|Figure 6: Alpha vector norm map of the tampered image. High valued blocks correspond nicely to tampered regions.]]

imported>Projects221 at 07:39, 21 March 2013

2013-03-21T07:39:56Z

← Older revision		Revision as of 07:39, 21 March 2013
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	For our EM algorithm, we set the neighborhood of interpolation to be 1, so we get 8 <math>\alpha</math> coefficients that make up an <math>\overrightarrow{\alpha}</math> for each block in every color channel. What we did is find the median <math>\overrightarrow{\alpha}</math> of the image, and compute the norm of every <math>\overrightarrow{\alpha}</math> associated with every block with this median value. The idea behind this is that for tampered regions, the resulting norm values would be large, since the tampered regions would have the most different <math>\overrightarrow{\alpha}</math> values compared to the rest of the image.		For our EM algorithm, we set the neighborhood of interpolation to be 1, so we get 8 <math>\alpha</math> coefficients that make up an <math>\overrightarrow{\alpha}</math> for each block in every color channel. What we did is find the median <math>\overrightarrow{\alpha}</math> of the image, and compute the norm of every <math>\overrightarrow{\alpha}</math> associated with every block with this median value. The idea behind this is that for tampered regions, the resulting norm values would be large, since the tampered regions would have the most different <math>\overrightarrow{\alpha}</math> values compared to the rest of the image.
	Here is the same example difference image as shown above, where the tampered region is shown, highlighted in the yellow box.		Here is the same example difference image as shown above, where the tampered region is shown, highlighted in the yellow box.
	[[File:diff_nc.png\|350px\|center]]<br>		[[File:diff_nc.png\|350px\|center\|thumb\|Figure 5: Example difference image between real and tampered version. The tampered region is show in the yellow box.]]<br>
	Below we have shown the map of the computed norms for this image, and we can see that the high value regions correspond well to the tampered region in the difference image.		Below we have shown the map of the computed norms for this image, and we can see that the high value regions correspond well to the tampered region in the difference image.
	[[File:alpha_maxs.png\|650px\|center]]		[[File:alpha_maxs.png\|650px\|center\|thumb\|Figure 6: Alpha vector norm map of the tampered image. High valued blocks correspond nicely to tampered regions.]]

	===Clustering Algorithm===		===Clustering Algorithm===

imported>Projects221: /* Fourier Transform data */

2013-03-21T07:38:30Z

Fourier Transform data

← Older revision		Revision as of 07:38, 21 March 2013
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	[[File:diff_nc.png\|350px\|thumb\|center\|Figure 3: Example difference image between real and tampered version. The tampered region is show in the yellow box.]]<br>		[[File:diff_nc.png\|350px\|thumb\|center\|Figure 3: Example difference image between real and tampered version. The tampered region is show in the yellow box.]]<br>
	Below we have shown the "FFT peak" map for this image, and we can see that the low value regions correspond well to the tampered region in the difference image.		Below we have shown the "FFT peak" map for this image, and we can see that the low value regions correspond well to the tampered region in the difference image.
	[[File:fft_mins.png\|650px\|center\|thumb}Figure 4: FFT peak map of the tampered image. Low valued blocks correspond nicely to tampered regions.]]		[[File:fft_mins.png\|650px\|center\|thumb\|Figure 4: FFT peak map of the tampered image. Low valued blocks correspond nicely to tampered regions.]]

	===Alpha vectors===		===Alpha vectors===

imported>Projects221: /* Fourier Transform data */

2013-03-21T07:38:15Z

Fourier Transform data

← Older revision		Revision as of 07:38, 21 March 2013
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	Here we show an example of image of the difference between a real image and a tampered version of the image, where the tampered region is shown, highlighted in the yellow box.		Here we show an example of image of the difference between a real image and a tampered version of the image, where the tampered region is shown, highlighted in the yellow box.

	[[File:diff_nc.png\|350px\|center\|Figure 3: Example difference image between real and tampered version. The tampered region is show in the yellow box.]]<br>		[[File:diff_nc.png\|350px\|thumb\|center\|Figure 3: Example difference image between real and tampered version. The tampered region is show in the yellow box.]]<br>
	Below we have shown the "FFT peak" map for this image, and we can see that the low value regions correspond well to the tampered region in the difference image.		Below we have shown the "FFT peak" map for this image, and we can see that the low value regions correspond well to the tampered region in the difference image.
	[[File:fft_mins.png\|650px\|center\|Figure 4: FFT peak map of the tampered image. Low valued blocks correspond nicely to tampered regions.]]		[[File:fft_mins.png\|650px\|center\|thumb}Figure 4: FFT peak map of the tampered image. Low valued blocks correspond nicely to tampered regions.]]

	===Alpha vectors===		===Alpha vectors===