Rate-distortion models for error resilient video transcoding

1. A method for transcoding a video, comprising:

modeling a requantization of an input video as a first rate-distortion function of an input video;

modeling a resynchronization marker insertion rate as a second rate-distortion function of the input video;

modeling an intra-block insertion as a third rate-distortion function of the input video; and

transcoding the input video according to the first, second and third rate-distortion functions to produce an output video, in which the input video has a first bit rate greater than a second bit rate of the output video, and a distortion D is expressed as

D

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L

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Φ

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where L is a total number of frequency coefficients of a discrete cosine transform in the input video, Φ(ω i ) is a power spectrum density function of coefficient i, R is the second bit rate, and β is 21n2.

2. The method of claim 1 , further comprising:

allocating bits of the input video to the output video according to the first, second, and third rate-distortion models.

3. The method of claim 1 , in which the first rate-distortion function outputs a quantization parameter, the second rate-distortion function outputs the resynchronization marker insertion rate, and the third rate-distortion function outputs the intra-block insertion rate.

4. The method of claim 1 , in which inter-frame dependencies in the output video are due to a requantization distortion in a current frame of the output video that is propagated to a next frame of the output video through motion compensation, and further comprising:

modifying the first rate-distortion model for the next frame to account for propagating the requantization distortion.

5. The method of claim 2 , in which β is a variable, R(D) is replaced by R γ (D), where γ is a Lagrange multiplier, and [Π i=0 L−1 Φ(ω i )] 1/L is replaced by a variance σ 2 , so that the distortion is

D=σ 2 e −βR γ (D) .

6. The method of claim 5 , in which β is in a range of [1, 10], and γ is in a range of [0, 1], so that the distortion is

D 0 =σ 0 2 e −β 0 R 0 γ0 ,

where D 0 is a distortion of an intra-coded frame of the output video caused by the requantization, and R 0 is the first bit rate.

7. The method of claim 6 , further comprising:

estimating β and γ from two sample points on the first, second and third rate-distortion functions.

8. The method of claim 6 , in which the allocating operates on groups-of-frames of the output video to account for inter-frame dependencies in the input video due to a requantization distortion in a current frame of the output video that is propagated to a next frame of the output video through motion compensation, and further comprising:

changing the variance σ 2 k to σ *2 k to model the inter-frame dependency, in which a distortion of requantized inter-frames is

D k =σ* k 2 e −β k R k γ =(σ k 2 +α k D k-1 ) e −β k R k γ , k= 1, 2 , . . . , N− 1,

where σ *2 k =σ 2 k +α k D k-1 , and D k-1 denotes a quantization residue error produced when a previous frame of the input video is requantized with a larger quantization-scale, α k denotes a propagation ratio, which is determined by an amount of motion compensation, α k D k-1 models the inter-frame dependency between the current and the previous frame, and N is a total number of frames in a group-of-frames.

9. The method of claim 2 , in which the bits allocated for inserting the resynchronization markers are determined from a number of bits in a resynchronization header and a resynchronization marker spacing, and the bits allocated for inserting the intra-blocks are determined from the intra-block insertion rate and an average rate increase by replacing inter-coded block with intra-blocks.