Neuroimaging - Revision history

imported>Projects221: /* Explanation */

2013-03-26T00:47:00Z

Explanation

← Older revision		Revision as of 00:47, 26 March 2013
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	<b> 2.</b> In order to calculate the cross correlation the Fourier transform of each file is needed. Using functions such as ‘fftn’ and ‘fftshift,’ the Fourier transform of each file is taken. <br>		<b> 2.</b> In order to calculate the cross correlation the Fourier transform of each file is needed. Using functions such as ‘fftn’ and ‘fftshift,’ the Fourier transform of each file is taken. <br>

	<b> 3.</b> Cross-correlation~~</b>~~: The maximum value of the cross-correlation is simply multiplying the Fourier transform of one file by the conjugate of the Fourier transform of the second file and then determining the maximum value. This then returns a non-normalized single value that is characteristic of how well the maximum value their image alike.<br>		<b> 3.</b> Cross-correlation: The maximum value of the cross-correlation is simply multiplying the Fourier transform of one file by the conjugate of the Fourier transform of the second file and then determining the maximum value. This then returns a non-normalized single value that is characteristic of how well the maximum value their image alike.<br>

	<b>4.</b> In order to normalize the cross-correlation, the product of the sum of the all the pixel intensities was taken. Then each maximum value from the cross-correlation was divided by the product of the sum of the vectors. This allows for the maximum value of the cross-correlation of an image with itself to be one.<br>		<b>4.</b> In order to normalize the cross-correlation, the product of the sum of the all the pixel intensities was taken. Then each maximum value from the cross-correlation was divided by the product of the sum of the vectors. This allows for the maximum value of the cross-correlation of an image with itself to be one.<br>

imported>Projects221: /* Cross-Correlation */

2013-03-25T21:46:03Z

Cross-Correlation

← Older revision		Revision as of 21:46, 25 March 2013
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	It is maximized at the shift amount at which the signals are most similar. Therefore, a signal cross-correlated with itself, the autocorrelation, is maximized at the origin. A signal cross-correlated with a shifted version of itself is maximized at the translation amount. The maximum value of the cross-correlation provides a measure of the similarity of the two functions independent of any shifting between them. Since, for the brain-matching portion of this project, the goal is to determine if two images are of the same brain, regardless of any translation between the two acquisitions, we chose to use the maximum of the cross-correlation. <br><br>		It is maximized at the shift amount at which the signals are most similar. Therefore, a signal cross-correlated with itself, the autocorrelation, is maximized at the origin. A signal cross-correlated with a shifted version of itself is maximized at the translation amount. The maximum value of the cross-correlation provides a measure of the similarity of the two functions independent of any shifting between them. Since, for the brain-matching portion of this project, the goal is to determine if two images are of the same brain, regardless of any translation between the two acquisitions, we chose to use the maximum of the cross-correlation. <br><br>

	The maximum value of the cross-correlation, however, is affected by the amplitudes of f and g (in our case, the intensities of the two brain MRIs being compared.) Because our algorithm should identify two MRIs of the same brain even if they have different brightness levels (intensities), we normalize the cross-correlation maximum value before using it as our similarity metric. The cross-correlation maximum is divided by the square root of the product of the image energies. The image energy is defined as the autocorrelation at the origin, or <br>		The maximum value of the cross-correlation, however, is affected by the amplitudes of f and g (in our case, the intensities of the two brain MRIs being compared). Because our algorithm should identify two MRIs of the same brain even if they have different brightness levels (intensities), we normalize the cross-correlation maximum value before using it as our similarity metric. The cross-correlation maximum is divided by the square root of the product of the image energies. The image energy is defined as the autocorrelation at the origin, or <br>

	[[ File: image004.gif ]] <br>		[[ File: image004.gif ]] <br>

imported>Projects221: /* Brain Matching Results */

2013-03-25T21:20:14Z

Brain Matching Results

← Older revision		Revision as of 21:20, 25 March 2013
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	</center>		</center>

	Overall, our results show that our brain matching algorithm has no false positive matches and is robust to noise and translation.		Overall, our results show that our brain matching algorithm has no false positive matches and is robust to noise and translation. Pending the availability of a dataset with multiple MRIs of the same brains, we plan to test our algorithm's ability to detect these matches.

	== Conclusions ==		== Conclusions ==

imported>Projects221: /* Brain Matching Results */

2013-03-25T21:16:49Z

Brain Matching Results

← Older revision		Revision as of 21:16, 25 March 2013
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	</center>		</center>

			Overall, our results show that our brain matching algorithm has no false positive matches and is robust to noise and translation.

	== Conclusions ==		== Conclusions ==

imported>Projects221: /* Brain Matching Results */

2013-03-25T21:14:26Z

Brain Matching Results

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	=== Brain Matching Results ===		=== Brain Matching Results ===
	The normalized cross-correlation maximum was the metric used to quantify the similarity between MRIs. This similarity between twelve randomly chosen brain MR scans are shown in the table below. This data illustrates that the values between two distinct files fall below the similarity metric threshold of 0.9 while the values of the same files are 1 (as expected due to the normalization). Therefore, ~~this~~ is a		The normalized cross-correlation maximum was the metric used to quantify the similarity between MRIs. This similarity between twelve randomly chosen brain MR scans are shown in the table below. This data illustrates that the values between two distinct files fall below the similarity metric threshold of 0.9 while the values of the same files are 1 (as expected due to the normalization). Therefore, 0.9 is a
	reasonable choice of threshold. <br><br>		reasonable choice of threshold. <br><br>

	[[File: Randomvsself_Table_xCorValues.jpg\|SNR - Random Vs Self\|center]] <br>		[[File: Randomvsself_Table_xCorValues.jpg\|SNR - Random Vs Self\|center]] <br>

	The results from adding white Gaussian noise to a randomly chosen brain MRI and comparing two different noise-added versions of the same scan are shown in the next figure. The noisy images simulate two different acquisitions of the same brain. The normalized cross-correlation maximums are plotted against the SNR of the added noise. The left plot shows the results of the cross-correlation algorithm with no pre-processing of the MRIs while the right plot shows the results from median filtering prior to cross correlation. This illustrates that, using the filtered algorithm, the images are identified as coming from the same brain ~~as long as the SNR is above approximately 7~~ (the similarity metric falls above the threshold of 0.9), a significant improvement over the unfiltered algorithm. <br> <br>		The results from adding white Gaussian noise to a randomly chosen brain MRI and comparing two different noise-added versions of the same scan are shown in the next figure. The noisy images simulate two different acquisitions of the same brain. The normalized cross-correlation maximums are plotted against the SNR of the added noise. The left plot shows the results of the cross-correlation algorithm with no pre-processing of the MRIs while the right plot shows the results from median filtering prior to cross correlation. This illustrates that, using the filtered algorithm, the images are identified as coming from the same brain (the similarity metric falls above the threshold of 0.9) as long as the SNR is above approximately 7, a significant improvement over the unfiltered algorithm. <br> <br>

	<center>		<center>

imported>Projects221: /* Cross-Correlation */

2013-03-25T21:09:30Z

Cross-Correlation

← Older revision		Revision as of 21:09, 25 March 2013
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	==== Cross-Correlation ====		==== Cross-Correlation ====

	In signal processing, cross-correlation, also known as a sliding dot product or sliding inner-product, is a measure of the similarity of two waveforms as a function of a translation applied to one of them. More formally, the 3D discrete cross-correlation of n x m x p functions f(x, y, z) and g(x, y, z) is <br>		In signal processing, cross-correlation, also known as a sliding dot product or sliding inner-product, is a measure of the similarity of two waveforms as a function of a translation applied to one of them. More formally, the 3D discrete (circular) cross-correlation of n x m x p functions f(x, y, z) and g(x, y, z) is <br>

	[[ File: image002.gif ]] <br><br>		[[ File: image002.gif ]] <br><br>

imported>Projects221: /* Andrew Zabel */

2013-03-22T16:19:51Z

Andrew Zabel

← Older revision		Revision as of 16:19, 22 March 2013
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	Exploration of additional filtering before cross-correlation (integrating band-pass filter and cross-correlation codes)<br>		Exploration of additional filtering before cross-correlation (integrating band-pass filter and cross-correlation codes)<br>
	Wiki: <br>		Wiki: <br>
	• Algorithm and Filtering ~~Explanation~~ sections <br>		• Writing of Algorithm Explanation and Filtering sections <br>
	• Editing of some sections <br>		• Editing of some sections <br>

imported>Projects221: /* Andrew Zabel */

2013-03-22T16:19:22Z

Andrew Zabel

← Older revision		Revision as of 16:19, 22 March 2013
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	Idea for using 3D Fourier transforms <br>		Idea for using 3D Fourier transforms <br>
	Exploration of additional filtering before cross-correlation (integrating band-pass filter and cross-correlation codes)<br>		Exploration of additional filtering before cross-correlation (integrating band-pass filter and cross-correlation codes)<br>
	Editing of some sections ~~of the Wiki~~ <br>		Wiki: <br>
			• Algorithm and Filtering Explanation sections <br>
			• Editing of some sections <br>

	=== Acknowledgements ===		=== Acknowledgements ===

imported>Projects221: /* Future Scope */

2013-03-22T10:28:47Z

Future Scope

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	<b>a)</b> Apply Wolberg and Zokai's robust image registration using log-polar transform to correct for any scaling and rotation [[#References\|[4]]] Scale and rotate one of the images by the appropriate amount in order to match the other image.<br><br>		<b>a)</b> Apply Wolberg and Zokai's robust image registration using log-polar transform to correct for any scaling and rotation [[#References\|[4]]] Scale and rotate one of the images by the appropriate amount in order to match the other image.<br><br>

	<b>b)</b> Then apply our normalized cross-correlation-based brain matching algorithm to determine the similarity between the two brains. <br>		<b>b)</b> Then apply our normalized cross-correlation-based brain matching algorithm to determine the similarity between the two brains. <br><br>
	For step (a), the algorithm will have to be adapted to work in three dimensions rather than two. This should not be theoretically difficult. Spherical coordinates can be used instead of polar coordinates, still taking the log of the radial coordinate. Then, a cross-correlation that is linear in the log(r) direction and circular in the theta and phi directions will provide information on the scaling and rotation factors between the two images. The numerous 3D interpolations and cross-correlations implicit in this method, however, may pose a computational challenge. Therefore, the feasibility of making the brain matching algorithm robust to scaling and rotation should be investigated in the future if it is likely for MRIs to be rotated or scaled.		For step (a), the algorithm will have to be adapted to work in three dimensions rather than two. This should not be theoretically difficult. Spherical coordinates can be used instead of polar coordinates, still taking the log of the radial coordinate. Then, a cross-correlation that is linear in the log(r) direction and circular in the theta and phi directions will provide information on the scaling and rotation factors between the two images. The numerous 3D interpolations and cross-correlations implicit in this method, however, may pose a computational challenge. Therefore, the feasibility of making the brain matching algorithm robust to scaling and rotation should be investigated in the future if it is likely for MRIs to be rotated or scaled.

imported>Projects221: /* Future Scope */

2013-03-22T10:27:46Z

Future Scope

← Older revision		Revision as of 10:27, 22 March 2013
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	<b>a)</b> Apply Wolberg and Zokai's robust image registration using log-polar transform to correct for any scaling and rotation [[#References\|[4]]] Scale and rotate one of the images by the appropriate amount in order to match the other image.<br><br>		<b>a)</b> Apply Wolberg and Zokai's robust image registration using log-polar transform to correct for any scaling and rotation [[#References\|[4]]] Scale and rotate one of the images by the appropriate amount in order to match the other image.<br><br>

	<b>b)</b> Then apply our normalized cross-correlation-based brain matching algorithm to determine the similarity between the two brains.		<b>b)</b> Then apply our normalized cross-correlation-based brain matching algorithm to determine the similarity between the two brains. <br>
	For step (a), the algorithm will have to be adapted to work in three dimensions rather than two. This should not be theoretically difficult. Spherical coordinates can be used instead of polar coordinates, still taking the log of the radial coordinate. Then, a cross-correlation that is linear in the log(r) direction and circular in the theta and phi directions will provide information on the scaling and rotation factors between the two images. The numerous 3D interpolations and cross-correlations implicit in this method, however, may pose a computational challenge. Therefore, the feasibility of making the brain matching algorithm robust to scaling and rotation should be investigated in the future if it is likely for MRIs to be rotated or scaled.		For step (a), the algorithm will have to be adapted to work in three dimensions rather than two. This should not be theoretically difficult. Spherical coordinates can be used instead of polar coordinates, still taking the log of the radial coordinate. Then, a cross-correlation that is linear in the log(r) direction and circular in the theta and phi directions will provide information on the scaling and rotation factors between the two images. The numerous 3D interpolations and cross-correlations implicit in this method, however, may pose a computational challenge. Therefore, the feasibility of making the brain matching algorithm robust to scaling and rotation should be investigated in the future if it is likely for MRIs to be rotated or scaled.