Intra - Revision history

EPirat: Fix formula using unicode character. Seems Math is displayed once rendered and once as text for some reason.

2015-05-26T21:16:09Z

Fix formula using unicode character. Seems Math is displayed once rendered and once as text for some reason.

← Older revision		Revision as of 21:16, 26 May 2015
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	This is slightly complicated by the fact that our coefficients are not in the time-domain, but are the result of a lapped transform, see [[TDLT]]. In practice all of these modes have an equivalent in the frequency domain. As a starting point, we are using the 10 modes from VP8 to classify the blocks from a set of sample images. Each category of blocks will be used to construct a set of predictors <math>\beta</math> which is then used to reclassify the blocks based on Sum of Absolute Transform Differences (SATD). <i>Tim suggested weighting each blocks contribution based on SATD_bestfit-SATD_nearest</i>.		This is slightly complicated by the fact that our coefficients are not in the time-domain, but are the result of a lapped transform, see [[TDLT]]. In practice all of these modes have an equivalent in the frequency domain. As a starting point, we are using the 10 modes from VP8 to classify the blocks from a set of sample images. Each category of blocks will be used to construct a set of predictors <math>\beta</math> which is then used to reclassify the blocks based on Sum of Absolute Transform Differences (SATD). <i>Tim suggested weighting each blocks contribution based on SATD_bestfit-SATD_nearest</i>.

	== ~~<math>L^2</math>~~ -norm ==		== L²-norm ==

	Suppose for some mode we have <math>n</math> blocks. We can then construct the matrices <math>X</math> and <math>Y</math> where the ith row of each contains the zero-mean values from the ith block.		Suppose for some mode we have <math>n</math> blocks. We can then construct the matrices <math>X</math> and <math>Y</math> where the ith row of each contains the zero-mean values from the ith block.

EPirat at 21:13, 26 May 2015

2015-05-26T21:13:22Z

← Older revision		Revision as of 21:13, 26 May 2015
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	This is slightly complicated by the fact that our coefficients are not in the time-domain, but are the result of a lapped transform, see [[TDLT]]. In practice all of these modes have an equivalent in the frequency domain. As a starting point, we are using the 10 modes from VP8 to classify the blocks from a set of sample images. Each category of blocks will be used to construct a set of predictors <math>\beta</math> which is then used to reclassify the blocks based on Sum of Absolute Transform Differences (SATD). <i>Tim suggested weighting each blocks contribution based on SATD_bestfit-SATD_nearest</i>.		This is slightly complicated by the fact that our coefficients are not in the time-domain, but are the result of a lapped transform, see [[TDLT]]. In practice all of these modes have an equivalent in the frequency domain. As a starting point, we are using the 10 modes from VP8 to classify the blocks from a set of sample images. Each category of blocks will be used to construct a set of predictors <math>\beta</math> which is then used to reclassify the blocks based on Sum of Absolute Transform Differences (SATD). <i>Tim suggested weighting each blocks contribution based on SATD_bestfit-SATD_nearest</i>.

	== <math>L^2</math>-norm ==		== <math>L^2</math> -norm ==

	Suppose for some mode we have <math>n</math> blocks. We can then construct the matrices <math>X</math> and <math>Y</math> where the ith row of each contains the zero-mean values from the ith block.		Suppose for some mode we have <math>n</math> blocks. We can then construct the matrices <math>X</math> and <math>Y</math> where the ith row of each contains the zero-mean values from the ith block.

EPirat at 21:12, 26 May 2015

2015-05-26T21:12:17Z

← Older revision		Revision as of 21:12, 26 May 2015
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	\right)		\right)
	</math>		</math>

	~~Test~~

	~~<math>E=mc^2</math>~~

	Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.		Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.

EPirat at 18:06, 26 May 2015

2015-05-26T18:06:51Z

← Older revision		Revision as of 18:06, 26 May 2015
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	Test		Test

	<math>E=mc^2*2</math>		<math>E=mc^2</math>

	Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.		Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.

EPirat at 17:56, 26 May 2015

2015-05-26T17:56:15Z

← Older revision		Revision as of 17:56, 26 May 2015
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	Test		Test

	<math>E=mc^2</math>		<math>E=mc^2*2</math>

	Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.		Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.

EPirat at 16:53, 26 May 2015

2015-05-26T16:53:31Z

← Older revision		Revision as of 16:53, 26 May 2015
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	\right)		\right)
	</math>		</math>

			Test

			<math>E=mc^2</math>

	Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.		Assuming a linear predictor, we would like to find the 768 coefficients that best predict <math>y_i</math> from the neighboring <math>x_i</math>. That is, for a given block with coefficients <math>\hat x</math> and <math>\hat y</math>, we would like a 48x16 matrix <math>\beta</math> such that the residual <math>\hat e=\hat y-\hat x \beta</math> is minimized (for some <math>p</math>-norm). Because it is this residual <math>\hat e</math> that is quantized and coded in the bitstream, we would prefer that most of its coefficients are zero. This will be discussed further when comparing the different <math>p</math>-norms.

EPirat at 11:52, 27 April 2015

2015-04-27T11:52:21Z

← Older revision		Revision as of 11:52, 27 April 2015
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	Pooled Blocks 16591925 SATD 5466.77 Bits 636.877 Mean 1868.35 Var 720473 CgRef 15.3899 CgPred 16.0271 Pg 0.63723		Pooled Blocks 16591925 SATD 5466.77 Bits 636.877 Mean 1868.35 Var 720473 CgRef 15.3899 CgPred 16.0271 Pg 0.63723
	</pre>		</pre>




	[1] http://blog.webmproject.org/2010/07/inside-webm-technology-vp8-intra-and.html		[1] http://blog.webmproject.org/2010/07/inside-webm-technology-vp8-intra-and.html

	[[Category:Daala]]		[[Category:Daala]]

EPirat at 11:44, 27 April 2015

2015-04-27T11:44:07Z

← Older revision		Revision as of 11:44, 27 April 2015
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	\end{array}		\end{array}
	\right)		\right)

	</math>		</math>

EPirat at 11:43, 27 April 2015

2015-04-27T11:43:51Z

← Older revision		Revision as of 11:43, 27 April 2015
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	\end{array}		\end{array}
	\right)		\right)

	</math>		</math>

MrZeus at 23:02, 5 January 2015

2015-01-05T23:02:45Z

← Older revision		Revision as of 23:02, 5 January 2015
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	[1] http://blog.webmproject.org/2010/07/inside-webm-technology-vp8-intra-and.html		[1] http://blog.webmproject.org/2010/07/inside-webm-technology-vp8-intra-and.html

			[[Category:Daala]]