Xinqiao Liu Rate constrained conditional replenishment

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Rate-Constrained Conditional Replenishment with Adaptive

Change Detection

Xinqiao Liu

December 8, 2000

EE368B Project

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Motivation

• Conditional replenishment ---- method of reducing temporal redundancy between successive frames

– Efficient in video conferencing with stationary cameras and slow motion.

– Study shows that less than 3% of the pixels need to be replenished in most head-and-shoulders scenes in desktop video

• Computational complexity is significant simpler than other video compression methods– Software-only CODEC is possible

– Appealing for on-sensor compression where pixel array and simple image processing are integrated on the same chip, i.e, camera system-on-chip

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Previous Work

• Most of the research concentrate mainly on the image quality (Haskell,

et al’72, Haskell’79)

• Recently, a perception-based change detection method was proposed

(Chiu&Berger ’96, Chiu&Berger’99)

– Reduces the perceptual redundancy in addition to the spatial and temporal redundancy

– Change detection threshold is set based on Web’s law

• However, the correlation between transmission bit-rate and the choice

of change detection schemes still need to be explored.

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Outline

• Introduction & Problem formulation

• Context-based Arithmetic Encoder

• Change detection --- direct methods

– Subsampling

– Threshold adjusting

• Adaptive change detection

– Noise characteristic

– Adaptive algorithm

• Conclusion

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Conditional Replenishment Diagram

Goal: Given a rate-constrained transmission channel, find the optimal change detection algorithm that minimizes the distortion

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Model and Assumptions

Assumptions:1. Transmitted separately under certain bit-rate constrain R1, R2 2. Lossless coding for both mask and signal3. Only intra-frame compression is considered

Current frame

Change detector

Change mask

Changed signal

CAE encoder

Signal encoder

Current frame

Change mask

Changed signal

CAE decoder

Signal decoder

Frame store Frame

store

Channel #1, rate = R1

Channel #2, rate = R2

#1

#2

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Rate-Constrained Change Detection

• Three ways to control the bit rate in the change detector:

1. Subsampling the mask and signal after detection

2. Adjusting the detection threshold

3. Using adaptive threshold for each pixel based on the noise characteristics -----eliminate those pixels that have changed due to noise rather than the input

• Use unconstrained Lagrangian cost function to find the optimum detection parameters for each method

Change mask

ABS Average of 3x3 window

Threshold

Previous frame

Current frame

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Problem Formulation (I)

CACAA 212 )1(ˆ

The mean-square distortion is defined as: 2

212

2222 ))1(()ˆ()ˆ,( CACAEAAEAAD

The above assumption allows us to study the rate-distortion function of conditional replenishment by only implementing the compression scheme of the mask.

Assume R1 = kR2 since they are proportional to the number of changed

pixels. The total bit-rate R is

1221 )1()()( RkCAHCHRRR

Given previous frame A1, current frame A2, binary change mask C, the reconstructed frame at decoder end is:

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Problem Formulation (II)The constrained problem of:

)()(),( sRsDsJ

Can be converted to the unstrained problem by introducing the Lagrangian cost function given Lagrange multiplier :

max222 osubject t )ˆ|)ˆ,(min( RRAAAD

0),(

s

sJ

where s is the adjustable change detection parameter. The optimal

value of s is given by:

The desired optimal slop value is not known a priori but can be obtained using a fast bisection search algorithm

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Outline

• Introduction & problem formulation

• Context-based Arithmetic Encoder

• Change detection --- direct methods

• Adaptive change detection

• Conclusion

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Test Video Sequence

• Captured by a stationary high-speed digital camera with a person moving cross the screen:

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Context-based Arithmetic Encoder (CAE)

• Binary bitmap-based shape coding scheme used in the MPEG-4 standard

• Three types of 16x16 macroblocks:

– "black" block: none of the pixel changed (all 0)

– "white" block: all pixels changed and to be replenished (all 1)

– “boundary” block: encoded with a template of 10 pixels to define the causal context for predicting the binary value of the current pixel (S0).

S8 S9 S10

S3 S4 S5 S6 S7

S2 S1 S0 )),,(log(),,,(),,|( 1010101010210

100 1

ssspssspSSSSHss s

For black and white blocks, only the block type need to be transmitted

For boundary blocks, use conditional entropy:

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Outline

• Introduction & problem formulation

• Context-based Arithmetic Encoder

• Change detection --- direct methods

– Subsampling

– Threshold adjusting

• Adaptive change detection

• Conclusion

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Change Masks With Subsampling • Subsample the macroblock by a factor of 2, 4 or 8

• Subblocks are encoded using the CAE

• Upsample at the decoder end using pixel replication filter combined with a 3x3 median filter

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Rate-distortion of Subsampling

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Change Masks With Threshold-adjusting

• Control the bit-rate by globally adjusting the change detector threshold. As the threshold increased, few pixels will be detected

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Rate-distortion of Threshold-adjusting

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Outline

• Introduction & problem formulation

• Context-based Arithmetic Encoder

• Change detection --- direct methods

• Adaptive change detection

– Noise characteristics

– Adaptive algorithm

• Conclusion

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Noise Characteristics

• A fundamental problem in designing an optimum change detector is how to separate pixels whose change is due to noise from pixels whose change is due to real input signal change

• For cameras using either CCD or CMOS image sensors, the final image is formed by the photo-charge Qi,j (or voltage) integrated on each photo-detector

during the exposure time. Two independent additive noise corrupt the output signal:

– Shot noise Ui,j which is zero mean signal dependent gaussian distribution

with:

– Readout circuit and reset noise Vi,j (including quantization noise) with

zero mean and variance V

.

),0(~ ,, jiji qQNU

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Adaptive Change Detection

• Thus the total noise variance of pixel (i,j) is:

– The noise is signal dependent

– The stronger the luminance level, the noisier the pixel will be

• The threshold Ti,j is thus set as:

– where m is the sensitivity factor that is set globally

– is local average value over a small area with size 8x8.

• Note that by changing m, we effectively adjusting the detection sensitivity while the threshold is still locally adapted

2,,

2Vjiji qQ

2,,, Vjijiji QqmmT

jiQ ,

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Adaptive Threshold

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Change Masks With Adaptive Threshold

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Rate-distortion of Adaptive Threshold

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Performance Comparison

•Subsampling is the most efficient in reducing bit-rate•Adaptive thresholding achieves the best PSNR

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Conclusion

• Studied three change detection algorithms:

1. Subsampling

2. Threshold-adjusting

3. Adaptive threshold based on the noise characteristics

• The adaptive change detection algorithm efficiently separates pixels whose change is due to noise from pixels whose value change is due to real input signal change

• Simulation proves that the adaptive change detection algorithm achieves the best PSNR among all the three algorithms