# Patent

## Title
Optimal intra prediction in block-based video coding

## Abstract

Selection of an optimal directional intra prediction mode for block-based video coding from a reduced number of intra predictions, including a plurality of angular intra predictions, a planar prediction mode, and DC prediction mode, by performing a logarithmic search inside a set of intra prediction directions.

## Background
This application is divisional of U.S. patent application Ser. No. 13/679,161, filed Nov. 16, 2012, which claims benefit of U.S. Provisional Application No. 61/560,556, filed Nov. 16, 2011, both of which are hereby incorporated herein by reference in their entirety.


FIELD OF THE INVENTION
This application relates to video encoding systems, preferably to methods for making coding decisions and estimating coding parameters for using in video coding standards, in particular, in High Efficiency Video Coding (HEVC) specifications for video compression.
BACKGROUND OF THE INVENTION
Video encoding is employed to convert an initial video sequence (a set of video images, also named pictures, or frames) into a corresponding encoded bitstream (a set of compressed video sequence binary data), and also converting video sequence binary data produced by a video codec system into a reconstructed video sequence (a decoded set of video images, or reconstructed frames). Most video coding standards are directed to provide the highest coding efficiency, which is the ability to encode a video sequence at the lowest bit rate while maintaining a certain level of video quality.
Most video sequences contain a significant amount of statistical and subjective redundancy within and between pictures that can be reduced by data compression techniques to make its size smaller. First the pictures in the video sequence are divided into blocks. The latest standard, the High Efficiency Video Coding (HEVC) uses blocks of up to 64×64 pixels and can sub-partition the picture into variable sized structures. HEVC initially divides a picture into coding tree units (CTUs), which are then divided into coding tree blocks (CTBs) for each luma/chroma component. The CTUs are further divided into coding units (CUs), which are then divided into prediction units (PUs) of either intra-picture or inter-picture prediction type. All modern video standards including HEVC use a hybrid approach to the video coding combining inter-/intra-picture prediction and 2D transform coding.
The intra-coding treats each picture individually, without reference to any other picture. HEVC specifies 33 directional modes for intra prediction, wherein the intra prediction modes use data from previously decoded neighboring prediction blocks. The prediction residual is the subject of Discrete Cosine Transform (DCT) and transform coefficient quantization.
The inter-coding is known to be used to exploit redundancy between moving pictures by using motion compensation (MC), which gives a higher compression factor than the intra-coding. According to known MC technique, successive pictures are compared and the shift of an area from one picture to the next is measured to produce motion vectors. Each block has its own motion vector which applies to the whole block. The vector from the previous picture is coded and vector differences are sent. Any discrepancies are eliminated by comparing the model with the actual picture. The codec sends the motion vectors and the discrepancies. The decoder does the inverse process, shifting the previous picture by the vectors and adding the discrepancies to produce the next picture. The quality of a reconstructed video sequence is measured as a total deviation of it's pixels from the initial video sequence.
In common video coding standards like H.264 and HEVC (High Efficiency Video Coding) intra predictions for texture blocks include angular (directional) intra predictions and non-angular intra predictions (usually, in DC intra prediction mode and Planar prediction mode). Angular intra prediction modes use a certain angle in such a way that for texture prediction the data of the neighboring block pixels is propagated to the block interior at such angle. Due to the sufficient amount of possible intra prediction angles (e.g. 33 in HEVC specification) the procedure of choosing the optimal intra prediction may become very complex: the most simple way of the intra prediction mode selection is calculating all the possible intra predictions and choosing the best one by SAD (Sum of Absolute Difference), Hadamard SAD, or RD (Rate Distortion) optimization criterion.
However, the computational complexity of this exhaustive search method grows for a large number of possible prediction angles. To avoid an exhaustive search, an optimal intra prediction selection procedure is important in the video encoding algorithms. Moreover, the nature of the modern block-based video coding standards is that they admit a large variety of coding methods and parameters for each texture block formation and coding. Accommodating such a need requires selecting an optimal coding mode and parameters of video encoding.
The HEVC coding standard, however, extends the complexity of motion estimation, since the large target resolution requires a high memory bandwidth; large blocks (up to 64×64) require a large local memory; an 8-taps interpolation filter provides for a high complexity search of sub-pixel; and 1⁄2 and 3⁄4 non-square block subdivisions require complex mode selection.
SUMMARY
The above needs and others are at least partially met through provision of the methods pertaining to selection of an optimal intra prediction mode and partitions, and to motion estimation for inter coding described in the following description.
Methods for Choosing the Optimal Intra Coding Mode.
The methods described by Algorithm 1 and Algorithm 2 set forth herein are used for reducing the set of possible optimal intra predictions (testing sets) in the HEVC algorithm. Algorithm 3 and Algorithm 4 as appear in the present application provide low complexity methods for associating the appropriate intra prediction angle with the texture block using the concept of Minimal Activity Direction. The present application also teaches an efficient method of selecting the optimal intra prediction mode which is provided by Algorithm 5. The method of choosing the best intra block subdivision in HEVC (Algorithm 6) is based on calculation of the Minimal Activity Directions.
Inter Coding Methods: Calculation for Fast Motion Estimation and Optimal Block Partition.
The HEVC specification assumes a huge number of options when texture partitioning into inter coded blocks, each of which can have its own motion vector for inter texture prediction. Choosing the optimal partitions and the optimal motion vector requires advanced methods for the texture motion estimation and analysis. The present application provides integral methods for texture motion analysis targeted for usage in the HEVC video coding. These methods include the motion analysis for all possible partitions of the entire Coding-Tree Unit (CTU) and yield the motion vectors for all those partitions together with the recommendations for texture inter coding partition. The motion analysis method for the partitions of the entire Coding Unit Tree is provided in the Algorithm 7 described herein, while Algorithm 8 (described below) provides the multi-pass motion vectors refinement and Algorithm 9 (also described below) provides local transform-based motion estimation.
The system is targeted mainly to the HEVC specifications for video compression. Those skilled in the art, however, will appreciate that most of the described algorithms (both for intra and inter coding) may be used in conjunction with other video coding standards as well.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a flow diagram of angular intra prediction directions in the HEVC specification.
FIG. 2 shows testing sets Q for intra-prediction according to Algorithm 2
FIGS. 3A-3B illustrate a Minimal Activity Directions concept.
FIG. 4 shows a flow diagram of calculating direction intra prediction mode using pre-calculated tables.
FIG. 5 shows a flow diagram of choosing the best intra mode using a minimal activity direction calculation.
FIG. 6 is a flow diagram showing preparation of a reduced resolution image.
FIG. 7 comprises a block diagram.



DETAILED DESCRIPTION
Generally speaking, pursuant to the following various embodiments, the encoding methods are directed to: searching for optimal angular prediction in an intra-prediction mode based on minimal activity directions; choosing the best intra block subdivision using minimal activity directions and strengths; and providing motion estimation for tree-structured inter coding of the HEVC specifications. Certain actions and/or steps may be described or depicted in a particular order of occurrence while those skilled in the art will understand that such specificity with respect to sequence is not actually required. The terms and expressions used herein have the ordinary technical meaning as is accorded to such terms and expressions by persons skilled in the technical field as set forth above except where different specific meanings have otherwise been set forth herein.
Presented below are the preferred embodiments (algorithms) for each of the methods. Though preferred, it will be understood that these embodiments are offered for illustrative purposes and without any intent to suggest any particular limitations in these regards by way of the details provided.
Selection of Optimal Angular Intra Prediction Mode in Block-Based Video Coding
These teachings are directed to simplify the way of choosing the best directional intra prediction modes in block-based video coding. By way of illustration, FIG. 1 depicts the intra-prediction directions as provided by the HEVC specification. However, the proposed method is not limited to HEVC and can be applicable with corresponding evident modifications to any set of the directional intra predictions.
The angular intra predictions corresponding to the directions in FIG. 1 are defined as P0, P1, . . . , P32, the corresponding angles as γ0, γ1, . . . γ32, and the planar and DC prediction mode as P33, P34, respectively. The prediction cost function R(Pj) represents the best mode selection. It may be SAD function; Hadamard SAD function; Rate-Distortion-based cost function, and so forth. The smaller is the value of R(Pj), the more preferable the prediction Pj.
The intra predictions corresponding to the directions P0, P1, . . . , P32 are represented by the following sets:
S32={P16};
S16={P8, P24};
S8={P8, P16, P24, P32};
S4={P0, P4, P8, P12, P16, P20, P24, P28, P32};
S2={P0, P2, P4, P6, P8, P10, P12, P14, P16, P18, P20, P22, P24, P26, P28, P30, P32}.
One efficient way to significantly restrict the number of checked intra predictions is to use a logarithmic search inside a set of intra prediction directions. One corresponding method, which is described by Algorithm 1, comprises:
(i) selecting a starting set of intra prediction directions, a value Lε{32, 16, 8, 4, 2} and a cost function R(PK), depending on the desired speed and coding quality, where K is the index of this intra prediction;
(ii) from the set SL, finding an intra prediction providing the minimal value of the cost function R(P);
(iii) finding an intra prediction which minimizes the value of R(P) over Pε{PK, PK−L/2, PK+L/2};
(iv) setting a threshold T0, which is a pre-defined parameter depending on a desired speed, quality, block size, and so forth;

    
    
        if K=2, or R(PK)<T0, going to the next step; otherwise, performing step (iii) for L=L/2;
    
    


(v) if K=2, selecting an optimal intra prediction from a set {PK, PK−1, PK+1, P33, P34} as a prediction minimizing the value R(P); otherwise the optimal intra prediction is R(PK).
Another approach to efficiently restricting the search is initially checking a small number of intra predictions, and constructing the testing set of the intra prediction angles around the best angle from the initial subset. This approach can significantly reduce the number of tests and is described below as Algorithm 2:

    
    
        select an initial set {P0, P8, P16, P24, P32} for finding an intra prediction PK minimizing the value of cost function R(P), wherein K is the index of this intra prediction;
        set a threshold T0, which is a pre-defined parameter of the method depending on desired speed, quality, block size, and so forth;
        if R(PK)<T0, the optimal prediction is PK, and no further action is required;
        if R(PK)≧T0, proceed to test the following sets of intra predictions:
        
            Q0={P32, P0, P1, P2, P3, P5, P6};
            Q8−={P4, P5, P6, P7, P8, P9, P10};
            Q8+={P6, P7, P8, P9, P10, P11, P12};
            Q16−={P12, P13, P14, P15, P16, P18, P19};
            Q16+={(P14, P15, P16, P17, P18, P19, P20};
            Q24−={P20, P21, P22, P23, P24, P25, P26};
            Q24+={P22, P23, P24, P25, P26, P27, P28};
            Q32={P0, P27, P28, P29, P30, P31, P32}.
        
        
        choose the intra prediction set Q according to the following requirements:
        if K=0 or K=32, the intra prediction set Q=QK;
        if K≠0 and K≠32, then:
        
            if R(PK−8)<R(PK+8), Q=QK−; and
            if R(PK−8)≧R(PK+8); Q=QK+; and
        
        
        find the optimal intra prediction from the set Q=QK∪{P33, P34}, as the one minimizing the value of R(P).
    
    


Accordingly, the present method significantly reduces the number of intra predictions to be checked. The sets Q0, Q8−, Q8+, Q16−, Q16+, Q24−, Q24+, Q32 may also be constructed as some subsets of those defined above according to the desired speed, quality, or other measure of interest.
Method of Choosing a Best Intra Prediction Mode Based on Texture Gradient Analysis
These teachings are based on analyzing the distribution of texture gradients inside a texture block and on its reconstructed boundaries. It is based on a concept of Minimal Activity Direction (MAD) introduced in this description. A minimal activity direction is defined herein as a direction inside the area S in which the variation of a function P(x,y) is minimal. In particular, if the function P(x,y) represents the pixel brightness values of N×M picture, the minimal activity direction of the picture area is the direction of the most noticeable boundaries and lines inside a selected area S. The greater is the minimal activity direction strength, the brighter the corresponding line over the background. If the area S consists of a single point, the minimal activity direction is just the direction orthogonal to the gradient vector at this point.
FIGS. 3A and 3B illustrate the concept of minimal activity direction. FIG. 3A illustrates the minimal activity direction for optimal intra prediction: FIG. 3A (a) shows the initial block; 3A(b)—the gradient vector g and minimal activity direction o for a single point; 3A(c)—the minimal activity directions for the whole block. In FIG. 3B the picture is divided into 16×16 blocks, and the minimal activity directions are drawn for all of them for the case of equal weights W. Therefore, the minimal activity directions may be used in selection of the optimal intra prediction.
In this section some auxiliary terms and notations are provided.
Let's introduce the following notations:

    
    
        P(x,y) is a discrete function of two arguments defined at the rectangular set of integer pairs R={ 0,N−1}×{ 0,M−1};
        S is a set of integer coordinate pairs (x,y); S⊂R;
        W(x,y) is a set of non-negative weight coefficients defined at (x,y)εS (in the simplest case, the value of non-negative weight W(x,y) may be chosen to be equal to 1);
        DX(x,y)=(P(x+1,y)−P(x−1,y))/2; and
        DY(x,y)=(P(x,y+1)−P(x,y−1))/2;

where Dx(x,y) is any measure of P(x,y) function variation with respect to the first argument, and Dy (x,y) is any measure of P(x,y) function variation with respect to the second argument in the neighborhood of the (x,y) point.

    
    


Let's assume that ΣW(x,y)·DX2 (x,y)+ΣW(x,y)·DY2 (x,y)≠0 and find a minimal activity direction defined by a vector (α(S,W),β(S,W)), which will be the solution of the following minimization problem:




  
    
      
        ∑
        
          
            (
            
              x
              ,
              y
            
            )
          
          ∈
          S
        
      
      ⁢
      
        
          W
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        ·
        
          
            (
            
              
                α
                ·
                
                  
                    D
                    X
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
              
              +
              
                
              
              ⁢
              
                β
                ·
                
                  
                    D
                    Y
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
              
            
            )
          
          2
        
      
    
    -
    
      -
      
        α
        ⁣
        
          ,
          β
        
      
    
  
  ->
  min




wherein α2+β2=1.

Similarly, the minimal activity angle φ(S,W) can be found by solving the following minimization problem:




  
    ∑
    
      
        (
        
          x
          ,
          y
        
        )
      
      ∈
      S
    
  
  ⁢
  
    
      W
      ⁡
      
        (
        
          x
          ,
          y
        
        )
      
    
    ·
    
      
        
          (
          
            
              
                cos
                ⁡
                
                  (
                  φ
                  )
                
              
              ·
              
                
                  D
                  X
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
            
            +
            
              
                sin
                ⁡
                
                  (
                  φ
                  )
                
              
              ·
              
                
                  D
                  Y
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
            
          
          )
        
        2
      
      ⁢
      
        ⟶
        
          α
          ,
          β
        
      
      ⁢
      min
    
  




wherein α=cos(φ) and β=sin(φ).

The solution (α(S,W), β(S,W)) of the problem above is defined up to a certain precision, and the corresponding angle φ is defined up to a multiple of π. The corresponding angle φ can be calculated from (α(S,W), β(S,W)) for example as φ(S,W)=arccos(α(S,W)).
The direction defined by the vector (α(S,W), β(S,W)) or by the angle φ(S,W) is referred to herein as the minimal activity direction.
Calculating an Angular Intra Mode Defined by Minimal Activity Direction
For present purposes on may define the angular intra prediction modes as {P0, P1, . . . , PT-1}, and the corresponding prediction angles as {γ0, γ1, . . . , ≡T-1}. Using the minimal activity direction as defined above, one can calculate the following functions for a texture block B, where S is a spatial area which may coincide with B or include I, as follows:




  
    E
    =
    
      (
      
        
          
            ∑
            
              
                (
                
                  x
                  ,
                  y
                
                )
              
              ∈
              S
            
          
          ⁢
          
            
              W
              ⁡
              
                (
                
                  x
                  ,
                  y
                
                )
              
            
            ·
            
              
                D
                X
                2
              
              ⁡
              
                (
                
                  x
                  ,
                  y
                
                )
              
            
          
        
        -
        
          
            ∑
            
              
                (
                
                  x
                  ,
                  y
                
                )
              
              ∈
              S
            
          
          ⁢
          
            
              W
              ⁡
              
                (
                
                  x
                  ,
                  y
                
                )
              
            
            ·
            
              
                D
                Y
                2
              
              ⁡
              
                (
                
                  x
                  ,
                  y
                
                )
              
            
          
        
      
      )
    
  
  ,
  
    

  
  ⁢
  
    F
    =
    
      
        ∑
        
          
            (
            
              x
              ,
              y
            
            )
          
          ∈
          S
        
      
      ⁢
      
        
          W
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        ·
        
          
            D
            X
          
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        ·
        
          
            D
            Y
          
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
      
    
  
  ,
  
    

  
  ⁢
  
    A
    =
    
      
        
          E
          2
        
        
          
            E
            2
          
          +
          
            4
            ·
            
              F
              2
            
          
        
      
    
  




The calculations will be considered separately for the following four cases:
1. E≦0 and F<0;
2. E>0 and F<0;
3. E≧0 and F≧0; and
4. E<0 and F≧0.
It can be seen that the above four cases correspond to the following intervals of the angle φ(S,W) values: [0; π/4], [λ/4, λ/2], [λ/2, 3π/4] and [3λ/4, π], respectively.
Algorithm 3.
By this approach, the angular intra prediction modes can be calculated using the signs of E and F and the value of the ratio




  
    
    
      E
      F
    
    
  
  ⁢
  
    
  
  ⁢
  or
  ⁢
  
    
  
  ⁢
  
    
      
      
        F
        E
      
      
    
    .
  




Using this approach, one can define the case number j= 1,4 according to the values of E and F as described above.

The method comprises:
for each case, calculating the minimal activity direction (α(S,W), β(S,W)) as follows:



  
    
      1.
      ⁢
      
        
      
      ⁢
      For
      ⁢
      
        
      
      ⁢
      E
    
    ≤
    
      0
      ⁢
      
        
      
      ⁢
      and
      ⁢
      
        
      
      ⁢
      F
    
    <
    
      0
      ⁢
      
        :
      
    
  




  
    
      (
      
        
          
            
              α
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
        
          
            
              β
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
      
      )
    
    =
    
      (
      
        
          
            
              
                
                  (
                  
                    1
                    +
                    A
                  
                  )
                
                /
                2
              
            
          
        
        
          
            
              
                
                  (
                  
                    1
                    -
                    A
                  
                  )
                
                /
                2
              
            
          
        
      
      )
    
  




  
    
      2.
      ⁢
      
        
      
      ⁢
      For
      ⁢
      
        
      
      ⁢
      E
    
    >
    
      0
      ⁢
      
        
      
      ⁢
      and
      ⁢
      
        
      
      ⁢
      F
    
    <
    
      0
      ⁢
      
        :
      
    
  




  
    
      (
      
        
          
            
              α
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
        
          
            
              β
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
      
      )
    
    =
    
      (
      
        
          
            
              
                
                  (
                  
                    1
                    -
                    A
                  
                  )
                
                /
                2
              
            
          
        
        
          
            
              
                
                  (
                  
                    1
                    +
                    A
                  
                  )
                
                /
                2
              
            
          
        
      
      )
    
  




  
    
      3.
      ⁢
      
        
      
      ⁢
      For
      ⁢
      
        
      
      ⁢
      E
    
    ≥
    
      0
      ⁢
      
        
      
      ⁢
      and
      ⁢
      
        
      
      ⁢
      F
    
    ≥
    
      0
      ⁢
      
        :
      
    
  




  
    
      (
      
        
          
            
              α
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
        
          
            
              β
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
      
      )
    
    =
    
      (
      
        
          
            
              -
              
                
                  
                    (
                    
                      1
                      -
                      A
                    
                    )
                  
                  /
                  2
                
              
            
          
        
        
          
            
              
                
                  (
                  
                    1
                    +
                    A
                  
                  )
                
                /
                2
              
            
          
        
      
      )
    
  




  
    
      4.
      ⁢
      
        
      
      ⁢
      For
      ⁢
      
        
      
      ⁢
      E
    
    <
    
      0
      ⁢
      
        
      
      ⁢
      and
      ⁢
      
        
      
      ⁢
      F
    
    ≥
    
      0
      ⁢
      
        :
      
    
  




  
    
      (
      
        
          
            
              α
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
        
          
            
              β
              ⁡
              
                (
                
                  S
                  ,
                  W
                
                )
              
            
          
        
      
      )
    
    =
    
      (
      
        
          
            
              -
              
                
                  
                    (
                    
                      1
                      +
                      A
                    
                    )
                  
                  /
                  2
                
              
            
          
        
        
          
            
              
                
                  (
                  
                    1
                    -
                    A
                  
                  )
                
                /
                2
              
            
          
        
      
      )
    
  



calculating the corresponding angle φ(S,W)ε[0; π] as φ(S,W)=arccos(α(S,W));
finding γkε{γ0, γ1, . . . , γT-1} as intra prediction angle closest to the calculated minimal activity angle φ(S,W); and
choosing Pk as the intra prediction mode defined by the minimal activity direction calculated above.
Algorithm 4.
FIG. 4 shows another approach, in which an approximate calculation of the minimal activity directions and the corresponding angular intra prediction mode is performed using pre-calculated tables. This method comprises:

    
    
        considering some sufficiently large integers K and L defining the accuracy of the calculations (for example, both equal to 256);
        pre-calculating constant integer array AngleToMode[ ] of the size K+1 providing the correspondence between a prediction angle φε[0;π] and a prediction mode index P in the following way:

AngleToMode[round(K·φ/π)]=Pk,

wherein round(x) means rounding x to the closest integer;

        pre-calculating for each j= 1,4 four tables RatioToAngleDirect[j][ ] of the size L+1 providing the correspondence between the ratio |E/F|ε[0;1] and the prediction angle φε[0;π] in the following way:

RatioToAngleDirect[j][round(L·|E/F|)]=round(K·φ/π), wherein φε[0;π];

        pre-calculating for each j= 1,4 four tables RatioToAngleInverse[j][ ] of the size L+1 providing the correspondence between the ratio |F/E|ε[0;1] and the prediction angle φε[0;π] in the following way:

RatioToAngleInverse[j][round(L·|F/E|)]=round(K·φ/π), where φε[0;π];

        calculating the values E and F as described above;
        choosing the case number j= 1,4 according to the signs of E and F:
        if |E/F|ε[0;1], calculating the prediction mode Pk defined by the minimal activity direction as:

Pk=AngleToMode[RatioToAngleDirect[j][round(L·|E/F|)]];

        if |F/E|ε[0;1], calculate the prediction mode Pk defined by the minimal activity direction as:

Pk=AngleToMode[RatioToAngleInverse[j][round(L·|F/E|)]].

    
    


The tables RatioToAngleDirect and RatioToAngleInverse may be pre-calculated using explicit expressions for the minimal activity directions given above in this section.
Minimal Activity Direction Strengths
These teachings contemplate a set of the following values as the strength of the minimal activity direction defined by (α, β), where α2+β2=1:




  
    
      
        C
        1
      
      ⁡
      
        (
        
          α
          ,
          β
          ,
          S
          ,
          W
        
        )
      
    
    =
    
      
        
          ∑
          
            
              (
              
                x
                ,
                y
              
              )
            
            ∈
            S
          
        
        ⁢
        
          
            W
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          ·
          
            
              (
              
                
                  
                    -
                    β
                  
                  ·
                  
                    
                      D
                      X
                    
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If (α, β) defines the minimal activity direction for the block B with weights W, then the corresponding values of C1, C2 will be denoted simply as C1 (B,W), C2 (B,W) and will be called the minimal activity direction (MAD) strengths.
Simplifying the Optimal Intra Predictions Selection
A related video coding problem is to select the optimal intra prediction from a set of angular intra predictions for angles γ0, γ1 . . . γT-1 (enumerated monotonically clockwise or counterclockwise) as well as from DC and Planar predictions. A known most simple way to solve this problem is to calculate all possible intra predictions and choose the best mode by SAD, HAD or RD optimization criterion. These teachings provide a way of minimizing the number of intra predictions that need to be checked explicitly.
Algorithm 5.
FIG. 5 shows a flow diagram for a method of simplified selection of optimal intra prediction using the concept of minimal activity direction strength as introduced above. The method comprises:

    
    
        choosing a texture block B of the size L×L starting from pixel with coordinates (x,y), for which the intra prediction is to be selected;
        choosing a spatial area S including block B, wherein in the simplest case S may coincide with B;
        choosing the weights matrix for S, wherein in the simplest case all the weights w(j,k)=1;
        calculating the minimal activity direction and intra prediction mode mk defined by this direction as described above;
        defining a set Q of intra predictions to be checked for the optimal intra prediction selection as one including angular prediction mk, non-angular predictions (Planar prediction and/or DC prediction) and, optionally, some angular prediction modes corresponding to the angles neighboring to that defined by the mode Pk;
        defining constants X1, X2, X3 for parameters selected according to the desired speed and quality of the method;
        if the MAD strength C1({tilde over (B)},W)<X1, the angular predictions for the angles γk, γk−1, γk+1 may be excluded from the set Q; and
        if C1({tilde over (B)},W)>X2 and C2({tilde over (B)},W)<X3, the DC and planar predictions may be excluded from the set Q; and
        selecting the optimal intra prediction from the remaining set by a simple explicit check.
    
    


Choosing a Best Intra Block Size Based on Minimal Activity Directions and Strengths
Here one may select an intra block B of the size L×L starting from a pixel with coordinates (x,y) that can be predicted by the angular intra prediction for angles γ0, γ1 . . . γT-1 (enumerated monotonically clockwise or counterclockwise) and also by DC and Planar predictions. Instead of using L×L intra prediction, the block B may be divided into 4 sub-blocks Bj of the size




  
    
      L
      2
    
    ×
    
      L
      2
    
  
  ,




where jε[0,4], and each of these four blocks may be also intra predicted by an intra prediction from the same set of intra predictions. For the sake of an example, let's consider a problem of selecting the optimal block size between one whole block or a sub-block constructed by subdivision of the block into four sub-blocks.

The obvious solution for this problem is the exhaustive testing of all the possible options: all the admissible intra predictions for the block B, all the admissible intra predictions for the sub-blocks Bj, and then choosing the block best size by SAD or RD-optimization based criterion. It is also obvious that the computational complexity of this method is very high.
The present teachings are based on the concept of the minimal activity directions and are directed to simplify the method of choosing the best subdivision of a texture block into intra blocks.
Algorithm 6.
The method comprises:

    
    
        considering a texture block B of the size L×L starting from a pixel with coordinates (x,y), and its sub-blocks Bj, jε[0,4] of the size
    
    






  
    L
    2
  
  ×
  
    L
    2
  




starting from pixels with coordinates (x,y),





  
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respectively;

    
    
        constructing a spatial area S including the block B and the spatial areas Sj including blocks Bj, wherein in the simplest case S may coincide with B and Sj may coincide with Bj;
        calculating the minimal activity direction angles φ({tilde over (B)},W), φ({tilde over (B)},W), wherein α({tilde over (B)},W)=cos(φ({tilde over (B)},W)), β({tilde over (B)},W)=sin(φ({tilde over (B)},W));
        calculating functions of minimal activity direction (MAD) strength C1({tilde over (B)},W), C2({tilde over (B)},W), C1(α({tilde over (B)},W), β({tilde over (B)},W),{tilde over (B)}j,W), C2(α({tilde over (B)},W), β({tilde over (B)},W), {tilde over (B)}j,W), where jε[0,4]; and
        selecting a single L×L block as the best size, if the MAD strengths for all jε[0,4] are:
        C1(α({tilde over (B)},W),β({tilde over (B)},W),{tilde over (B)}j,W)<λ1+μ1·C1({tilde over (B)},W), and
        C2(α({tilde over (B)},W),β({tilde over (B)},W),{tilde over (B)}j,W)<λ2+μ2·C2({tilde over (B)},W),

wherein λ1, μ1, λ2, μ2 are pre-defined parameters of the encoding selected according to the desired speed and quality of the method;

        otherwise, selecting the size as a sub-division of block B into four
    
    






  
    L
    2
  
  ×
  
    L
    2
  




blocks.

Hierarchical Multi-Level Motion Estimation for Tree-Structured Inter Coding
The proposed methods are directed to reducing the complexity of the HEVC standard video coding without degrading the coding quality.
According to these teachings, the motion estimation starts from the largest block size allowed for the current frame and covers all the possible smaller block sizes in a single estimation process. The method uses a reduced resolution search in a motion estimation scheme based on Algorithm 7 (described below) with only one base motion vector field, wherein the interpolation is used only at the latest stage of motion estimation.
Motion Estimation Suitable for HEVC encoding
The present method chooses a block size 16×16 as a base block for motion estimation in HEVC encoding, because blocks 4×4 and 8×8 are too small and can introduce an error motion, and blocks 32×32 are too large and can introduce an averaging motion error.
The following proposed method of motion estimation may be used under the HEVC standard.
Algorithm 7.

    
    
        1. Prepare a reduced resolution image;
        2. Perform a reduced resolution search for blocks 64×64;
        3. Perform refinement by neighboring blocks;
        4. Provide a motion assignment for 16×16 blocks using neighboring blocks;
        5. Perform a refinement search for 16×16 blocks;
        6. Prepare error distribution (ED) analysis information for split-merge prediction and non-square block selection;
        7. Perform a sub-pixel refinement (without assigning vectors);
        8. Divide 16×16 blocks into 8×8 blocks;
        9. Merge four 16×16 blocks into one 32×32 partition;
        10. Merge four 32×32 blocks into one 64×64 partition;
        11. Provide a non-square block prediction using the ED field; and
        12. Assign quarter-pel to a selected decision.
    
    


The following approaches are used to optimize the proposed motion estimation method.
The reduced resolution search, which represents one step in a hierarchical search, is performed using reduced frames by four in both directions (X and Y), and performing reduced resolution search by blocks 16×16 using reduced frames in order to obtain motion for 64×64 blocks in the original frames.
A high quality motion vector field is prepared using Algorithm 8 (described below) for a multi-pass motion vector field refinement in order to obtain a very smooth and regular motion.
A fast motion search may be used in two stages of motion estimation by employing Algorithm 9 (described below) for integer motion estimation using non-parametric local transform.
A motion assignment for 16×16 blocks is performed using non-parametric local transform.
A problem of sub-dividing non-square blocks is herein solved by Algorithm 10 (described below) for choosing between splitting and merging certain blocks using error-distribution analysis.
The entire motion estimation is performed using integer-pel at all stages, and only after a decision is made, it may be refined to quarter-pel.
Multi-Pass Motion Vector Field Refinement
Algorithm 8.
After the motion estimation for a reduced resolution picture is completed, a method of refinement is proposed to make motion field more accurate, regular and smooth. This method comprises:
selecting a threshold T as a desired percent of all blocks in the picture;
setting a variable count C=0;
for every block in the picture:

    
    
        using motion vectors of eight neighbor blocks as candidate motion vectors;
        selecting a best motion vector MV by comparing SADs (sums of absolute difference) or any other distance metric; and
        if the vector has changed, incrementing variable count C; and
        if C<T, repeating the step of setting the count C.
    
    


This process can be performed multiple times before the number of motion vectors changed during a next pass is more than a selected threshold T.
Non-Parametric Local Transform Based Motion Estimation
Algorithm 9.
In performing steps (2) and (4) of Algorithm 7, it is necessary to find motion vectors in small reference frame area. Typically, the area is ±16 pixels. For such purpose one may perform a traditional block-matching procedure by calculating SAD (sum of absolute difference) or another distance metric for all possible positions. This process is very complex and requires an extended memory bandwidth.
However, using a proposed combination of simple filters and vector operations, the motion estimation may be performed without a need of actual block-matching process. In general, any suitable non-parametric local transform may be used as a base of the proposed motion estimation approach.
According to one embodiment, the Census transform is used as a base for algorithm description. The Census transform is a form of non-parametric local transform that relies on the relative ordering of local intensity values, and not on the intensity values themselves. This transform is usually used in image processing to map the intensity values of the pixels within a square window to a bit string, thereby capturing the image structure. The intensity value of a center pixel is replaced by the bit string composed of a set of Boolean comparisons in a square window moving left to right.
Accordingly, a new value of a center pixel (A′) calculated as a sum of bits is:

A′=(A<Zi)*2i,

where A is a previous value of center pixel; and

Zi represents the values of the neighboring pixels.

The Census-transformed image is used to find the correlation of pixels of the original block with the reference pixel area.
The proposed motion estimation algorithm may be divided into several stages:

    
    
        1. Performing Census transform for every input frame (gray, 8 bit/pixel);
        2. Splitting a frame into 16×16 blocks and representing it as a 256-bytes vector (M);
        3. Preparing a new 256-bytes vector (B), where at each position addressed by value from vector (A), its actual position in vector (A) is placed (index).
        4. Preparing a correlation surface filled with zeroes (32×32 bytes);
        5. Subtracting element-by-element vector (A) from vector (B);
        6. Returning into the two-dimensional space and incrementing points of the correlation surface at position given by a resulted vector (B′);
        7. Finding a maximum on the correlation surface, which requires a motion vector in full-pels; and
        8. Interpolating a sub-pixel value using neighbor values on the correlation surface.
    
    


Error Distribution Analysis
Algorithm 10.
After the actual search is done, for every block 8×8 one can calculate the appropriate SAD. For every block 64×64 pixels one has 8×8 block of SADs which can be referred to as Error Distribution Block (EDB). These teachings use the EDB concept for optimization of Split-Merge decisions.
The method of SPLIT decision optimization comprises:

    
    
        declaring SplitThreshold as a desired level of SPLIT sensitivity (in percents);
        calculating average SAD of the whole EDB;
        if any SAD in EDB differs from a calculated average SAD more than the SplitThreshold, marking said block as a SPLIT candidate; and
        performing an additional refinement search for every block marked as SPLIT candidate.
    
    


The method of MERGE decision optimization comprises:

    
    
        declaring a MergeThreshold as a desired level of MERGE sensitivity (in percents);
        preparing an EDB pyramid based on averaging 2×2 block of SADs at each level, wherein the pyramid comprises:
        
            Level 0: an original EDB of 8×8 SADs;
            Level 1: averaged once 4×4 SADs;
            Level 2: averaged twice 2×2 SADs; and
            Level 3: one averaged SAD.
        
        
        at every level from 1 to 3, examining four correspondence SADs to check MERGE flag;
        if all four SADs differ from lower level SAD no more than MergeThreshold, marking this block as a MERGE candidate;
        performing a MERGE check for every block marked as MERGE candidate by substituting four small blocks with one large block.
    
    


Reduced Resolution Image Preparation
Algorithm 11.
FIG. 6 illustrates the preparation of a reduced resolution image according to Algorithm 11. Every block 64×64 is represented as a 16×16 block. A shifted Gaussian filter is used herein for the reduced image preparation. Every pixel in reduced image (Zx/4,y/4) is calculated as a weighted sum of pixels in the original picture Ox,y:

Zx/4,y/4=(Ox,y+2*Ox+1,y+Ox+2,y+2*Ox,y+1+4*Ox+1,y+1+2*Ox+2,y+1+Ox,y+2+2*Ox+1,y+2±Ox+2,y+2)/16

This filter reduces computational complexity and provides better encoding quality by reducing the averaging effect as compared with traditional techniques (Simple Averaging, Gaussian Pyramid, and so forth).
Based on the above Algorithms 8-11, the following approach to Motion Estimation for Inter Coding is proposed:

    
    
        preparing a reduced resolution image using Algorithm 11;
        performing a reduced resolution search for blocks 64×64, preferably using Algorithm 9;
        performing a refinement by neighboring blocks, preferably using Algorithm 8;
        providing a motion assignment for 16×16 blocks using neighboring blocks;
        performing a refinement search for 16×16 blocks, preferably using Algorithm 9;
        preparing an error distribution (ED) analysis information for split-merge prediction and non-square block selection, preferably using Algorithm 10;
        performing a sub-pixel refinement (without assigning vectors);
        splitting 16×16 blocks into 8×8 blocks;
        merging four 16×16 blocks into one 32×32 partition using Algorithm 10;
        merging four 32×32 blocks into one 64×64 partition using Algorithm 10;
        providing non-square block prediction using ED field according to Algorithm 10; and
        assigning quarter-pel to a selected decision.
    
    


In a typical application setting, and referring now to FIG. 7, the various algorithms, steps, actions, and the like described herein can be carried out by a corresponding control circuit 701. Such a control circuit 701 can comprise a fixed-purpose hard-wired platform or can comprise a partially or wholly programmable platform. These architectural options are well known and understood in the art and require no further description here. This control circuit 701 is configured (for example, by using corresponding programming as will be well understood by those skilled in the art) to carry out one or more of the steps, actions, and/or functions described herein.
By one approach this control circuit 701 operably couples to a memory 702. This memory 702 may be integral to the control circuit 701 or can be physically discrete (in whole or in part) from the control circuit 701 as desired. This memory 702 can also be local with respect to the control circuit 701 (where, for example, both share a common circuit board, chassis, power supply, and/or housing) or can be partially or wholly remote with respect to the control circuit 701 (where, for example, the memory 702 is physically located in another facility, metropolitan area, or even country as compared to the control circuit 701).
This memory 702 can serve, for example, to non-transitorily store the computer instructions that, when executed by the control circuit 701, cause the control circuit 701 to behave as described herein. (As used herein, this reference to “non-transitorily” will be understood to refer to a non-ephemeral state for the stored contents (and hence excludes when the stored contents merely constitute signals or waves) rather than volatility of the storage media itself and hence includes both non-volatile memory (such as read-only memory (ROM) as well as volatile memory (such as an erasable programmable read-only memory (EPROM).)
The control circuit 701 can also operably couple, if desired, to a corresponding display 703 that can serve, for example, to depict the processed results as accord with these teachings.
The preceding description is intended to be illustrative of the principles of the invention, and it will be appreciated that numerous changes and modifications may occur to those skilled in the art, and it is intended in the appended claims to cover all those changes and modifications which fall within the true spirit and scope of the present invention.

## Claims

1. A method of selecting an optimal directional intra prediction mode in block-based video coding, comprising:
constructing a plurality of sets for angular intra predictions P0, P1, . . . , P32:
S32={P16};
S16={P8, P24};
S8={P0, P8, P16, P24, P32};
S4={P0, P4, P8, P12, P16, P20, P24, P28, P32};
S2={P0, P2, P4, P6, P8, P10, P12, P14, P16, P18, P20, P22, P24, P26, P28, P30, P32};
presenting planar prediction mode P33 and DC prediction mode P34; and
performing a logarithmic search inside a set of intra prediction directions to reduce a number of intra predictions to be tested for optimal intra prediction mode;
wherein the optimal mode Pj corresponds to a minimal value of a prediction cost function R(P).

2. The method of claim 1, wherein the logarithmic search comprises:
(i) from a plurality of sets of angular intra predictions selecting a set SL, a value Lε{32, 16, 8, 4, 2} and a cost function R(PK) depending on desired coding parameters;
(ii) from the set SL selecting an intra prediction PK providing the minimal value of cost function R(P), where K is an index for this intra prediction;
(iii) finding an intra prediction, which minimizes the value of R(P) over Pε{PK, PK−L/2, PK+L/2} and setting a value of index K for this intra prediction;
(iv) setting a pre-defined threshold T0 depending on desired coding parameters;
if K=2, or R(PK)<T0, going to step (v);
otherwise, performing step (iii) for L=L/2; and

(v) if K=2, selecting a best intra prediction from a set {PK, PK−1, PK+1, P33, P34} as a prediction minimizing the value of R(P);
otherwise, the optimal intra prediction is R(PK).

3. The method of claim 1, wherein reducing the number of intra predictions for testing comprises:
selecting an initial set containing a small number of intra predictions for testing;
selecting a best angle from the initial set of intra predictions; and
constructing a testing set of intra prediction angles around the best angle from the initial set.

4. The method of claim 3, wherein the initial set is S8={P0, P8, P16, P24, P32}.

5. The method of claim 4, further comprising:
from the initial set finding an intra prediction PK minimizing the value of a cost function R(P), where K is an index of the intra prediction;
setting a threshold T0, wherein T0 is a pre-defined coding parameter;
if R(PK)<T0, the optimal intra prediction is PK;
if R(PK)≧T0, testing the following sets of intra predictions:
Q0={P32, P0, P1, P2, P3, P5, P6};
Q8−={P4, P5, P6, P7, P8, P9, P10};
Q8+={P6, P7, P8, P9, P10, P11, P12};
Q16−={P12, P13, P14, P15, P16, P18, P19};
Q16+={P14, P15, P16, P17, P18, P19, P20};
Q24−={P20, P21, P22, P23, P24, P25, P26};
Q24+={P22, P23, P24, P25, P26, P27, P28};
Q32={P0, P27, P28, P29, P30, P31, P32};

choosing an intra prediction set Q according to the following requirements:
if K=0 or K=32, the intra prediction set Q=QK;
if K≠0 and K≠32, then:
if R(PK−8)<R(PK+8), Q=QK−; and
if R(PK−8)≧R(PK+8); Q=QK+; and

defining the optimal intra prediction PK from the set Q=QK∪{P33, P34}, as the one minimizing the value of R(P).

6. The method of claim 5, wherein the T0 is a pre-defined coding parameter depending on at least one of desired speed, quality and block size.

7. The method of claim 3, comprising constructing and testing a plurality of subsets Q0, Q8−, Q8+, Q16−, Q16+, Q24−, Q24+, Q32 according to desired coding parameters.

8. A video codec comprising a processor configured and arranged to select an optimal intra prediction mode by:
constructing a plurality of sets for angular intra predictions P0, P1, . . . , P32:
S32={P16};
S16={P8, P24};
S8={P0, P8, P16, P24, P32};
S4={P0, P4, P8, P12, P16, P20, P24, P28, P32};
S2={P0, P2, P4, P6, P8, P10, P12, P14, P16, P18, P20, P22, P24, P26, P28, P30, P32};
presenting planar prediction mode P33 and DC prediction mode P34; and
reducing a number of intra predictions to be tested for optimal intra prediction mode by performing a logarithmic search inside a set of intra prediction directions.

9. The video codec of claim 8, comprising a control circuit configured and arranged to perform the logarithmic search by:
(i) selecting from a plurality of sets of angular intra predictions: a set SL, a value Lε{32, 16, 8, 4, 2} and a cost function R(PK) depending on desired coding parameters;
(ii) selecting from the set SL an intra prediction PK providing the minimal value of cost function R(P), where K is an index for this intra prediction;
(iii) finding an intra prediction, which minimizes the value of R(P) over Pε{PK, PK−L/2, PK+L/2}, and setting a value of index K for this intra prediction;
(iv) setting a pre-defined threshold T0 depending on desired coding parameters;
if K=2, or R(PK)<T0, going to step (v);
otherwise, performing step (iii) for L=L/2; and

(v) if K=2, selecting a best intra prediction from a set {PK, PK−1, PK+1, P33, P34} as a prediction minimizing the value of R(P);
otherwise, the optimal intra prediction is R(PK).

10. The video codec according to claim 8, comprising a control circuit configured to reduce a number of intra predictions to be tested by:
selecting an initial set containing a small number of intra predictions for testing;
selecting a best angle from the initial set of intra predictions; and
constructing a testing set of intra prediction angles around the best angle from the initial set.

11. The video codec according to claim 10, wherein the control circuit is configured and arranged to reduce a number of intra predictions and to test them for optimal intra prediction mode by:
selecting from the initial set {P0, P8, P16, P24, P32} of intra predictions an intra prediction PK minimizing the value of a cost function R(P), where K is an index of the intra prediction;
setting a threshold T0, wherein T0 is a pre-defined coding parameter;
if R(PK)<T0, the optimal intra prediction is PK;
if R(PK)≧T0, testing the following sets of intra predictions:
Q0={P32, P0, P1, P2, P3, P5, P6};
Q8−={P4, P5, P6, P7, P8, P0, P10};
Q8+={P6, P7, P8, P9, P10, P11, P12};
Q16−={P12, P13, P14, P15, P16, P18, P19};
Q16+={P14, P15, P16, P17, P18, P19, P20};
Q24−={P20, P21, P22, P23, P24, P25, P26};
Q24+={P22, P23, P24, P25, P26, P27, P28};
Q32={P0, P27, P28, P29, P30, P31, P32};

choosing an intra prediction set Q according to the following requirements:
if K=0 or K=32, the intra prediction set Q=QK;
if K≠0 and K≠32, then:
if R(PK−8)<R(PK+8), Q=QK−; and
if R(PK−8)≧R(PK+8); Q=QK+; and

selecting from the set Q=QK∪{P33, P34} the optimal intra prediction PK minimizing the value of R(P).

12. The video codec according to claim 11, wherein the T0 is a pre-defined coding parameter depending on at least one of: desired codec speed, block size and quality of encoding.