1. Introduction to ME and DCT
2019/4/6
Introduction to ME and DCT
Variable Length Code
Discrete Cosine Transform
Motion Estimation
2019/4/6
ME & DCT VCLab

2. 2019/4/6
Compression Basics
Information entropy: Claude E. Shannon 1948, “A Mathematical Theory of Communication”
Lossless coding
Entropy coding methods: Huffman code, arithmetic code
Dictionary-based, LZ77(Lempel-Ziv)
PCM, Prediction coding, Differential PCM (DPCM)
Sub-band coding
Transform coding
Motion compensation
2019/4/6
ME & DCT VCLab

3. Outline Typical motion in videos The exercises of motion
2019/4/6
Outline
Typical motion in videos
The exercises of motion
Motion representation
How to find the Motion?
How to find the motion in a block?
Residuals
Block matching algorithms (BMAs)
Problems with BMA
Fast BMAs
Intra frame and inter frame
2019/4/6
ME & DCT VCLab

4. Typical Motion in Video Clips
2019/4/6
Typical Motion in Video Clips
Local motions
Global motions
Background
2019/4/6
ME & DCT VCLab

5. The Exercises of Motion
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The Exercises of Motion
Intra: Compress one frame independently
Each pixel has to be compressed.
DCT  Quantization  Binary coding
Inter: Compress one frame depending on the previous frame.
Background can be ignored.
Only compress moving objects and new objects
2019/4/6
ME & DCT VCLab

6. Example Compress and in frame 1.
2019/4/6
Example
Compress and in frame 1.
Compress the motion of in remaining frames.
Direction and magnitude
2019/4/6
ME & DCT VCLab 1 2 3 4

7. Motion Model Video Model & Format 3-D Motion Model 2-D Motion Model
2019/4/6
Motion Model
Video Model & Format
3-D Motion Model
2-D Motion Model
Constant intensity assumption & Optical flow model
2019/4/6
ME & DCT VCLab

8. Motion Model Object model, Illumination model & Camera model
2019/4/6
Motion Model
Object model, Illumination model & Camera model
ambient, point
diffuse reflection
2019/4/6
ME & DCT VCLab

9. 3-D Motion VS. 2-D Motion rigid: rotation & translation
2019/4/6
3-D Motion VS. 2-D Motion
rigid: rotation & translation
prospective projection
2019/4/6
ME & DCT VCLab

10. 2-D Motion Approximations
2019/4/6
2-D Motion Approximations
Approximations: affine (6 parameters) or bilinear model (8 parameters)
2019/4/6
ME & DCT VCLab

11. Constant Intensity Assumption & Optical Flow Equation
2019/4/6
Constant Intensity Assumption & Optical Flow Equation
Valid under:
Constant ambient illumination
Diffuse reflecting surface
Motion 
2019/4/6
ME & DCT VCLab

12. Motion Representation
2019/4/6
Motion Representation
Four types of motion info
Parameters: 2 (translation), 6 (affine) or 8 (bi-linear, projective)
Region-based
Global
Block-based
Pixel-based
2019/4/6
ME & DCT VCLab

13. 2019/4/6
How to Find the Motion?
2019/4/6
ME & DCT VCLab

14. 2019/4/6
How to Find the Motion?
Deformable BMA: node-based, affine (6 parameters) or bilinear model (8)
Mesh-based motion estimation
Region-based motion estimation
Multi-resolution approach
Overlapped motion estimation (H.263 optional)
Block matching: 2-D translation (2 parameters)
Assume all pixels in a block undergo a coherent motion, and
search for the motion parameters for each block independently.
2019/4/6
ME & DCT VCLab

15. Deformable BMA Node-based, affine (6 parameters) or bilinear model (8)
2019/4/6
Deformable BMA
Node-based, affine (6 parameters) or bilinear model (8)
Mesh-based motion estimation
2019/4/6
ME & DCT VCLab

16. Block-based VS. Mesh-based
2019/4/6
Block-based VS. Mesh-based
Block-based
Mesh-based
2019/4/6
ME & DCT VCLab

17. 2019/4/6
Region-based
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ME & DCT VCLab

18. Multi-resolution Approach
2019/4/6
Multi-resolution Approach
2019/4/6
ME & DCT VCLab

19. Overlapped Motion Estimation
2019/4/6
H.263
2019/4/6
ME & DCT VCLab

20. How to Find The Motion in A Block?
2019/4/6
How to Find The Motion in A Block?
Block matching
Occlusion
Frame i-1
Frame i
Motion vector
Reference frame
(existed)
Current frame
(to be encoded)
2019/4/6
ME & DCT VCLab
matched

21. 2019/4/6
Block Matching
Compare the difference between two blocks. (one is in the current frame, and the other is in the reference frame)
p = 1, sum of absolute difference
p = 2, mean square error | - |p
2019/4/6
ME & DCT VCLab
Candidate block
Current block

22. Objective Quality Measurement
2019/4/6
Objective Quality Measurement
Peak Signal to Noise Ratio (PSNR)
Other objective quality metrics, ITU-T Video Quality Experts Group (VQEG)
Currently, no objective measurement system is able to replace subjective testing, no one objective model outperforms the others in all cases.
2019/4/6
ME & DCT VCLab

23. Scan Line Order, MB by MB Scan Line Order Search Range Frame n-1
2019/4/6
Scan Line Order, MB by MB
Scan Line Order
Search Range
Frame n-1
Frame n
MV(1,0)
MV(0,0)
2019/4/6
ME & DCT VCLab

24. Residuals (1) occlusion Residuals motion 2019/4/6 2019/4/6
ME & DCT VCLab
Residuals
occlusion
motion

25. Residuals (2) Encoder (DCT  Quantization  Binary coding) DCT + Q
2019/4/6
Residuals (2)
Residual only
Encoder (DCT  Quantization  Binary coding)
Residuals
DCT + Q
iDCT + iQ
Motion
Compensation
Previous
Frame Buffer
2019/4/6
ME & DCT VCLab
MV = (dx, dy)

26. Residuals (3) Decoder Residual IDCT VLD MV Reconstructed frame Coded
2019/4/6
Residuals (3)
Decoder
Residual
IDCT
Reconstructed
frame
VLD
Coded
Bitstream MV
Motion
Compensation
Previous
Frame memory
2019/4/6
ME & DCT VCLab

27. Block Matching Algorithm - Full Search Method
2019/4/6
Block Matching Algorithm - Full Search Method
Scan line order 15 15
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ME & DCT VCLab

28. Problems with Block Matching (1)
2019/4/6
Problems with Block Matching (1)
Blocking effect (discontinuity across block boundary)
Because the block-wise translation model is not accurate
Real motion in a block may be more complicated than translation
There may be multiple objects with different motions in a block
Intensity changes may be due to illumination effect
Motion field somewhat chaotic
MVs are estimated independently from block to block
2019/4/6
ME & DCT VCLab

29. Problems with Block Matching (2)
2019/4/6
Problems with Block Matching (2)
3. Wrong MV in the flat region
Motion is indeterminate when spatial gradient is near zero
Motion vectors over picture boundaries
Motion is undefined in occluded regions
Requires tremendous computation
2019/4/6
ME & DCT VCLab

30. H.264 & Other Solutions H.264/AVC
2019/4/6
H.264 & Other Solutions
H.264/AVC
Variable-block-size motion estimation
1/4-, 1/8-pixel motion vector precision
Multiple reference pictures
Wavelet-based - Motion Compensated Temporal Filtering (MCTF)
Deformable BMA
Mesh-based motion estimation
Region-based motion estimation
Multi-resolution approach
Overlapped motion estimation
Fast algorithms
2019/4/6
ME & DCT VCLab

31. Complexity of Integer-Pel EBMA
2019/4/6
Complexity of Integer-Pel EBMA
Assumption
– Image size: M x M
– Block size: N x N
– Search range: (-R, R) in each dimension
– Search stepsize: 1 pixel (assuming integer MV)
• Operation counts (1 operation=1 “-”, 1 “+”, 1 “*”):
– Each candidate position: N2
– Each block going through all candidates: (2R+1)2 N2
– Entire frame: (M/N)2 (2R+1)2 N2 = M2 (2R+1)2
• Independent of block size!
• Example: M = 512, N = 16, R = 16, 30 fps
Total operation count = 2.85x108/frame = 8.55x109/second
• Regular structure suitable for VLSI implementation
• Challenging for software-only implementation
(2R+1)2N2
2019/4/6
ME & DCT VCLab

32. Fast Algorithms for BMA
2019/4/6
Fast Algorithms for BMA
(2R+1)2
Reduce # of search candidates:
• Only search for those that are likely to produce small errors.
• Predict possible remaining candidates, based on previous search result
Simplify the error measure (DFD) to reduce the computation involved for each candidate
2019/4/6
ME & DCT VCLab

33. Fast Block Matching Algorithms
2019/4/6
TSS
Three-Step Search Algorithm
BBGDS
Block-Based Gradient Descent Search Algorithm
NTSS
New 3-Step Search Algorithm DS
Diamond Search Algorithm
FSS
Four-Step Search Algorithm
In following slides, more fast block motion estimation techniques based on reducing the candidate blocks of checking points is portrayed. They are…
2019/4/6
ME & DCT VCLab

34. TSS (Three-Step Search Algorithm)
2019/4/6
TSS (Three-Step Search Algorithm)
The TSS is developing early in the the idea is perform on a 15x15 search area. At the initial step nine checking points include the center and 8 points which locate at the half distance between the edge of search area and the center are examined. If the best match block which has minimum MAE locates at the right-top corner, then the second steps is performed by center to the new checking points and another 8 checking which have only half distance corresponding to the pervious step are examined. Continually, the last 8 checking points are examined with half distance again on the minimum MAE checking points. When the best matching checking point is located at the center or reach the edge of the search area, the algorithm stops. For a 15x15 search area, the TSS always takes only three steps to complete the algorithm, that is why it called as a three steps search algorithm.
2019/4/6
ME & DCT VCLab

35. BBGDS (Block-Based Gradient Descent Search Algorithm)
2019/4/6
BBGDS (Block-Based Gradient Descent Search Algorithm)
In this slide an other gradient descent search algorithm is proposed. The BBGDS works like 4SS very much. But the distance of the center checking points and the other checking points is only 1 pixel. This searching scheme is very suitable for the slow motion sequences. But for the large motion sequence it is very inefficient because it may trap into a local minimum checking points.
2019/4/6
ME & DCT VCLab

36. NTSS (New 3-Step Search Algorithm)
2019/4/6
NTSS (New 3-Step Search Algorithm)
The new 3-step search algorithm is a combination of TSS and BBGDS. Since TSS is suitable for large motion and BBGDS is more suitable for slow motion contents. The NTSS first examines 17 checking points include the first step of TSS and the BBGDS pattern. If the best match is located at the inside checking points then the BBGDS search is perform otherwise the TSS is done for the rest steps.
2019/4/6
ME & DCT VCLab

37. NTSS (2) Decision 1: min at the search window center ?
2019/4/6
NTSS (2)
Decision 1: min at the search window center ?
Decision 2: min at one neighbor of center ?
1st step of NTSS
17 checking points
Decision 1
Decision 2
MV=0 T F
2nd step of NTSS
3 or 5 checking points
2nd and 3rd step of NTSS
(same as in TSS)
IEEE Transactions on Circuits and Systems for Video Technology, June 1994.
2019/4/6
ME & DCT VCLab

38. FSS (Four-Step Search Algorithm)
2019/4/6
FSS (Four-Step Search Algorithm)
The differences between TSS and FSS is that the TSS downscale the checking points distance per step. But the FSS uses same distance to move the checking pattern. The algorithm start at zero motion checking points and 8 checking points with distance 2 pixels. If the minimum is located at the upper middle point. Then only additional three checking points need to be joined for next step comparison. If the minimum MAE is located at the corner position, then five new checking points need to addin. Finally when the checking points is near by the edge of search area, the distance is reduced to 1 pixel.
In a 15 by 15 search area, the 4SS takes at most 4 steps to get convergences. That is the same reason it called 4 step search algorithm.
2019/4/6
ME & DCT VCLab

39. DS (Diamond Search Algorithm)
2019/4/6
DS (Diamond Search Algorithm)
2019/4/6
ME & DCT VCLab

40. Adaptive Search Patterns
2019/4/6
Adaptive Search Patterns
TSS + DS + BBGDS
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ME & DCT VCLab

41. Fractional Pixel Accuracy
2019/4/6
Fractional Pixel Accuracy
Fractional pixel accuracy
e.g., half-pixel accuracy
Integer pixel
half pixel
H.263, Foreman, QCIF
SKIP=2, Q=4,5,7,10,15,25
(dx, dy) = (1.5, 1)
2019/4/6
ME & DCT VCLab

42. 2019/4/6
Exercise #1
1. Calculate the total amount of computations of EBMA for H.264 per P frame of size 19201088.
Due: March 28
2019/4/6
ME & DCT VCLab

43. Introduction to ME and DCT
2019/4/6
Introduction to ME and DCT
Motion Estimation
Discrete Cosine Transform
2019/4/6
ME & DCT VCLab

44. Outline Transform Coding Principles of Transform Coding
2019/4/6
Outline
Transform Coding
Principles of Transform Coding
Computation of Transform Coding
Discrete Fourier Transform
What Is DCT And Why Use DCT
How to Compute DCT
Program the DCT
2019/4/6
ME & DCT VCLab

45. 2019/4/6
Transform Coding
The picture is handled in a semi-parallel manner in blocks of elements. And it operates by generating a set of output data for each block in which the individual values are no longer correlated with one another and in which most of the energy of the original block is contained in a small proportion of the output samples.
Karhunen-Loeve transform (KLT)
Discrete and Fast Fourier transform
Hadamard transform
Discrete cosine transform
Wavelet transform
2019/4/6
ME & DCT VCLab

46. Principles of Transform Coding
2019/4/6
Principles of Transform Coding
Decorrelation: to generate less correlated or uncorrelated transform coefficients for greater or greatest efficiencies respectively.
Linearity: to allow a one-to-one mapping between the spatial and transform domains.
Orthogonality: the energy in both domains should be the same, and therefore no energy is either lost or carried redundantly.
2019/4/6
ME & DCT VCLab

47. Principles of Transform Coding
2019/4/6
Principles of Transform Coding
Sparsity (or energy compaction) in transformed domain: The energy in the transform domain tends always to be concentrated in the same subset of components, usually those representing low frequencies.
In mathematical terms, the analysis or first stage of the encoding process is a linear transformations that converts a set of highly correlated pixels with uniform probability density functions into a new set of less correlated coefficients with non-uniform pdfs.
2019/4/6
ME & DCT VCLab

48. Computation of Transform Coding
2019/4/6
Computation of Transform Coding
1-D transform
2-D transform: Usually 2-D transformation matrices are separable and the UV transform coefficients are derived from two 1-D transforms of lengths M and N. In implementation, this is done by
N times the 1-D transforms of M pixels in the line scan direction. This results in MN 1-D transform coefficients;
further M times the1-D transforms of the sets of N 1-D transform coefficients;
the final and true 2-D transform coefficients are then derived.
2019/4/6
ME & DCT VCLab

49. Discrete Fourier Transform
2019/4/6
Discrete Fourier Transform
Basis function:
N: the matrix length,
k: the frequency or sequence index of the basis vectors,
n: the pixel index.
Fast Fourier transform algorithm: requires O(nlog2n) time complexity.
Spurious spectral components are generated due to the implicit periodicity of the image blocks.
2019/4/6
ME & DCT VCLab

50. Discrete Cosine Transform
2019/4/6
Discrete Cosine Transform
The most efficient suboptimum transform
the elements of the kth basis vector: cos(k(2n+1)/2N)'s
It has the advantage over all other suboptimum transforms in that its basis vectors resemble closely the basis vectors of the KLT for smoothly varying video inputs. (for a first-order Markov source model)
The n-point DCT can be computed as a 2n-point DFT
2019/4/6
ME & DCT VCLab

51. Transform Coding System
2019/4/6
Transform Coding System
Input samples
Forward transform
Binary decoder
Quantizer
Inverse transform
÷10
Network
×10
Binary encoder
Inverse quantizer
e.g. zip, RAR
Huffman coding
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ME & DCT VCLab
Output samples

52. Representation of An Image
2019/4/6
Representation of An Image
How to code an image?
Spatial domain (pixel-based)
Transform domain
2019/4/6
ME & DCT VCLab

53. Why Use DCT? Properties of DCT
2019/4/6
Why Use DCT? Properties of DCT
Use cosine function as its basis function
Performance approaches KLT
Fast algorithm exists
Most popular in image compression applications
2019/4/6
ME & DCT VCLab

54. Does Transform Really Make Sense ?
2019/4/6
Does Transform Really Make Sense ?
Energy compaction
De-correlation: dependency elimination
2019/4/6
ME & DCT VCLab

55. An Example 8 8 2019/4/6 2019/4/6 ME & DCT 2008 VCLab 139 148 150 149
155
164
165
168 98
115
130
135
143
146
142
147 89
110
125
128
129
121
104
106 96
116
132
134
113
109
111
127
131
137
120
122
126
133
112
136
138
140
144
141 8 8
2019/4/6
ME & DCT VCLab

56. An Example A pixel expressed by it’s value
2019/4/6
An Example
A pixel expressed by it’s value
The coefficient of the basis vector (0,0)
DCT
IDCT
Pixel values in spatial domain
DCT coefficients in transform domain
2019/4/6
ME & DCT VCLab

57. Definition of DCT Basis Function
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Definition of DCT Basis Function
Basis function of the 1-D N-point DCT
For N = 8
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ME & DCT VCLab

58. 2019/4/6
An Example, N = 4
2019/4/6
ME & DCT VCLab

59. 2019/4/6
An Example, N = 4
2019/4/6
ME & DCT VCLab

60. An Example Represent a vector (e.g. a block of image samples) as the
2019/4/6
An Example
Represent a vector (e.g. a block of image samples) as the
superposition of some typical vectors (block patterns)
2019/4/6
ME & DCT VCLab

61. Basic diagram of DCT Discrete cosine transform and Inverse DCT (1) (2)
2019/4/6
Basic diagram of DCT
Discrete cosine transform and Inverse DCT
(1)
(2)
2019/4/6
ME & DCT VCLab

62. The Basis of 2D-DCT with 8x8 Block
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The Basis of 2D-DCT with 8x8 Block
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ME & DCT VCLab

63. Again – Do You Know What DCT Mean?
2019/4/6
Again – Do You Know What DCT Mean?
A pixel expressed by it’s value
The coefficient of the basis vector (0,0)
DCT
IDCT
Pixel values in spatial domain
DCT coefficients in transform domain
2019/4/6
ME & DCT VCLab

64. 2019/4/6
How to Compute: 1-D VS. 2-D
[1-D] For a M × N 2D-block, we can use 1D N-point DCT in the row direction, then the 1-D M-point DCT in the column direction to get the 2D-DCT
[2-D] If 8 × 8 blocks are applied, the 2D-DCT will be
2019/4/6
ME & DCT VCLab

65. DCT Matrix is Orthonormal
2019/4/6
DCT Matrix is Orthonormal
The above equation is zero if u≠ v orthogonal
The basis vector of DCT has unit norm
2019/4/6
ME & DCT VCLab

66. Energy Compaction of Orthormal Transform
2019/4/6
Energy Compaction of Orthormal Transform
2019/4/6
ME & DCT VCLab

67. Separable Transform (1/2)
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Separable Transform (1/2)
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ME & DCT VCLab

68. Separable Transform (2/2)
2019/4/6
Separable Transform (2/2)
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ME & DCT VCLab

69. 2019/4/6
Fast DCT algorithm (1/2)
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70. 2019/4/6
Fast DCT Algorithm (2/2)
2019/4/6
ME & DCT VCLab

71. How to program (1/3) - Basis
2019/4/6
How to program (1/3) - Basis
/***************************************************************************/
/*2D N*N DCT */
/*Input */
/*int argSource[N][N]：One block in the original image */
/*Output */
/*float argDCT[N][N]：The block in frequency domain corresponding to argSource[M][N] */
void DCT(int argDCT[8][8] , int argSource[8][8]) {
float C[8],Cos[8][8];
float temp;
int i,j,u,v;
for(i=0;i<8;i++)
for(j=0;j<8;j++)
Cos[i][j]=cos((2*i+1)*j*PI/16);
C[0]= ;
for(i=1;i<8;i++)
C[i]=0.5;
for(u=0;u<8;u++)
for(v=0;v<8;v++)
temp=0.0;
temp+=Cos[i][u]*Cos[j][v]*(argSource[i][j]-128);
temp*=C[u]*C[v];
argDCT[u][v]=temp; }
2019/4/6
ME & DCT VCLab

72. How to program (2/3) – A fast algorithm
2019/4/6
How to program (2/3) – A fast algorithm
/***************************************************************************/
/*2D N*N DCT */
/*Input */
/*int argSource[N][N]：One block in the original image */
/*Output */
/*float argDCT[N][N]：The block in frequency domain corresponding to argSource[M][N] */
void DCT(int argDCT[8][8] , int argSource[8][8]) {
float temp[8][8],temp1;
int i,j,k;
for(i=0;i<8;i++)
for(j=0;j<8;j++) {
temp[i][j] = 0.0; for(k=0;k<8;k++) temp[i][j] +=((int) argSource[i][k]-128)*Ct[k][j];
} for(i=0;u<8;u++)
for(j=0;v<8;v++)
temp1=0.0;
for(k=0;k<8;k++)
temp1+ =C[i][k] * temp[k][j];
argDCT[i][j]=ROUND(temp1); }
2019/4/6
ME & DCT VCLab

73. How to program (3/3) - for hardware implementation
2019/4/6
How to program (3/3) - for hardware implementation
#include <stdio.h>
#define RS(r,s) ((r) >> (s))
#define SCALE(exp) RS((exp),10)
void DCT(short int*input, short int*output) {
short int jc, i, j, k;
short int b[8];
short int b1[8];
short int d[8][8];
int c0=724;/* ; lect shift 10*/
int c1=502;
int c2=474;
int c3=426;
int c4=362;
int c5=284;
int c6=196;
int c7=100;
for (i = 0, k = 0; i < 8; i++, k += 8)
for (j = 0; j < 8; j++)
b[j] = input[k+j]; }
/* row transform */
for (j = 0; j < 4; j++)
jc = 7 - j;
b1[j] = b[j] + b[jc];
b1[jc] = b[j] - b[jc];
b[0] = b1[0] + b1[3];
b[1] = b1[1] + b1[2];
b[2] = b1[1] - b1[2];
b[3] = b1[0] - b1[3];
b[4] = b1[4];
b[5] = SCALE((b1[6] - b1[5]) * c0);
b[6] = SCALE((b1[6] + b1[5]) * c0);
b[7] = b1[7];
d[i][0] = SCALE((b[0] + b[1]) * c4);
d[i][4] = SCALE((b[0] - b[1]) * c4);
d[i][2] = SCALE(b[2] * c6 + b[3] * c2);
d[i][6] = SCALE(b[3] * c6 - b[2] * c2);
b1[4] = b[4] + b[5];
b1[7] = b[7] + b[6];
b1[5] = b[4] - b[5];
b1[6] = b[7] - b[6];
d[i][1] = SCALE(b1[4] * c7 + b1[7] * c1);
d[i][5] = SCALE(b1[5] * c3 + b1[6] * c5);
d[i][7] = SCALE(b1[7] * c7 - b1[4] * c1);
d[i][3] = SCALE(b1[6] * c3 - b1[5] * c5); }
/* column transform */
for (i = 0; i < 8; i++) {
for (j = 0; j < 4; j++) {
jc = 7 - j;
b1[j] = d[j][i] + d[jc][i];
b1[jc] = d[j][i] - d[jc][i];
b[0] = b1[0] + b1[3];
b[1] = b1[1] + b1[2];
b[2] = b1[1] - b1[2];
b[3] = b1[0] - b1[3];
b[4] = b1[4];
b[5] = SCALE((b1[6] - b1[5]) * c0);
b[6] = SCALE((b1[6] + b1[5]) * c0);
b[7] = b1[7];
d[0][i] = SCALE((b[0] + b[1]) * c4);
d[4][i] = SCALE((b[0] - b[1]) * c4);
d[2][i] = SCALE(b[2] * c6 + b[3] * c2);
d[6][i] = SCALE(b[3] * c6 - b[2] * c2);
b1[4] = b[4] + b[5];
b1[7] = b[7] + b[6];
b1[5] = b[4] - b[5];
b1[6] = b[7] - b[6];
d[1][i] = SCALE(b1[4] * c7 + b1[7] * c1);
d[5][i] = SCALE(b1[5] * c3 + b1[6] * c5);
d[7][i] = SCALE(b1[7] * c7 - b1[4] * c1);
d[3][i] = SCALE(b1[6] * c3 - b1[5] * c5); }
for (i = 0; i < 8; i++) { /* store 2-D array(8*8) data into a 1-D array (64)*/
for (j = 0; j < 8; j++) {
*(output + i*8 + j) = (d[i][j]);
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Conclusion
DCT provides a new method to express an image with the properties of the image
The fast algorithm provided for hardware implement is possible.
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Conclusion
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76. Reference Software H.264 MPEG-4 http://iphome.hhi.de/suehring/tml/
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Reference Software
H.264
MPEG-4
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Leakage Reduction (1)
It’s inherent in the DIGITAL Fourier transforms because of the required time domain truncation.
If the truncation interval is chosen equal to a multiple of the period, the frequency domain sampling function is coincided with the zeros of the sin(f)/f function do not alter the DFT results.
If the truncation interval is NOT chosen equal to a multiple of the period, the side-lobe characteristics of the sin(f)/f frequency function result additional frequency components (leakage) in DFT domain.
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Leakage Reduction (2)
To reduce this leakage it is necessary to employ a time domain truncation function which has side-lobe characteristics that are of smaller magnetite.
The Hanning function: The effect is to reduce the discontinuity, which results from the rectangular truncation function.
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