Appendix-Local-Warped-Motion.md

Top level

Local Warped Motion Compensation

1. Description of the algorithm

The warped motion mode is an inter-prediction mode where the prediction is generated by applying an (affine) transform to the reference. AV1 has two affine prediction modes: global warped motion and local warped motion (LW). The latter is discussed in more detail in the following.

AV1 has three types of motion modes that specify the motion of a block, namely SIMPLE, OBMC and LW. LW motion estimation provides a description of the type of local motion. Minimal signaling overhead is realized by signaling one flag in the inter block mode info, and that only under some conditions. LW cannot be combined with OBMC.

Warped motion compensation concerns the estimation and compensation of small local motion for a given block. The feature makes use of motion vector information for neighboring blocks to extract the affine local motion model parameters. The general motion model for local warped motion is given by

$\begin{bmatrix}x_r \\ y_r\end{bmatrix}= \begin{bmatrix}h_{11} & h_{12} & h_{13} \\ h_{21} & h_{22} & h_{23} \end{bmatrix}\begin{bmatrix}x \\ y \\ 1\end{bmatrix}$

where $\begin{bmatrix}x \\ y\end{bmatrix}$ and $\begin{bmatrix}x_r \\ y_r\end{bmatrix}$ represent the sample pixel coordinates in the current and reference frames, respectively. The decoder performs the same model estimation, so the encoder needs only to signal whether local warped motion is the selected mode for the current block and the corresponding translational model parameters $\mathbf{h_{13}}$ and $\mathbf{h_{23}}$, i.e. the rest of the model parameters are not signaled in the bitstream.

Model parameters $\mathbf{h_{13}}$ and $\mathbf{h_{23}}$ represent the entries in the current block motion vector ( $\mathbf{MV_0}$) in Figure 1 below).

Let $\mathbf{MV_0} = \begin{bmatrix}x_{mv} \\ y_{mv}\end{bmatrix}$
Then the above implies,
$\begin{bmatrix}h_{13} \\ h_{23}\end{bmatrix} = \begin{bmatrix}x_{mv} \\ y_{mv}\end{bmatrix}$,
The remaining parameters $h_{11}, h_{12}, h_{21}, h_{22}$ are estimated using a least squares approach.

To illustrate the estimation of these parameters, consider example shown in Figure 1 below.

Figure 1. Current block in yellow is a 32x32 block. Neighboring blocks that refer to the same reference picture as the current block are in blue. MVs (in orange) for the current block and the blue blocks are used to infer the local warp motion of the yellow block.

Let $C = \begin{bmatrix}x_0 \\ y_0\end{bmatrix}$ be the center of the current block, and $C' = \begin{bmatrix}x'_0 \\ y'_0\end{bmatrix}$ be the projection of $(C)$ onto the reference frame using the motion vector $\mathbf{MV_0}$ for the current block. According to the motion model:
$\begin{bmatrix}x'_0 \\ y'_0\end{bmatrix}= \begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{12}} & \color{blue}{h_{13}} \\ \color{orange}{h_{21}} & \color{orange}{h_{22}} & \color{blue}{h_{23}} \end{bmatrix}\begin{bmatrix}x_0 \\ y_0 \\ 1\end{bmatrix}$

where the translational component $\begin{bmatrix}\color{blue}{h_{13}}\\\color{blue}{h_{23}}\end{bmatrix}$ of the motion model would correspond to the motion vector $\mathbf{MV_0}$ for the current block. For block 7, define $C_7 = \begin{bmatrix}x_7 \\ y_7\end{bmatrix}$ to be the center of block 7, and $C'_7 = \begin{bmatrix}x'_7 \\ y'_7\end{bmatrix}$ to be the projection of $\mathbf{C}$ onto the reference frame using the motion vector $\mathbf{MV_7}$ for block 7.

The local warp transformation defines how the vector relating $\mathbf{C}$ and $\mathbf{C_7}$ in the source frame is mapped into the vector relating $\mathbf{C'}$ and $\mathbf{C'_7}$ in the reference frame.

$\begin{bmatrix}x'_7-x'_0 \\ y'_7 - y'_0\end{bmatrix}= \begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{12}} \\ \color{orange}{h_{21}} & \color{orange}{h_{22}} \end{bmatrix}\begin{bmatrix}x_7-x_0 \\ y_7 - y_0 \end{bmatrix}$

In addition to block 7, considering blocks 6 and 4 results in the following: $\begin{bmatrix}x'_4 - x'_0 & y'_4 - y'_0 \\ x'_6 - x'_0 & y'_6 - y'_0 \\ x'_7 - x'_0 & y'_7 - y'_0\end{bmatrix}= \begin{bmatrix}x_4 - x_0 & y_4 - y_0 \\ x_6 - x_0 & y_6 - y_0 \\ x_7 - x_0 & y_7 - y_0\end{bmatrix}\begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{21}} \\ \color{orange}{h_{12}} & \color{orange}{h_{22}} \end{bmatrix}$

Define, $V_1 = \begin{bmatrix}x'_4 - x'_0 \\ x'_6 - x'_0 \\ x'_7 - x'_0\end{bmatrix}, V_2 = \begin{bmatrix} y'_4 - y'_0 \\ y'_6 - y'_0 \\ y'_7 - y'_0\end{bmatrix}, R= \begin{bmatrix}x_4 - x_0 & y_4 - y_0 \\ x_6 - x_0 & y_6 - y_0 \\ x_7 - x_0 & y_7 - y_0\end{bmatrix}$

it follows that:
$\begin{bmatrix}V_1 & V2\end{bmatrix} = R\begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{21}} \\ \color{orange}{h_{12}} & \color{orange}{h_{22}} \end{bmatrix}$

Solving a least square estimation for $\begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{21}} \\ \color{orange}{h_{12}} & \color{orange}{h_{22}}\end{bmatrix}$ yields:

$\begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{21}} \\ \color{orange}{h_{12}} & \color{orange}{h_{22}} \end{bmatrix} = (R^TR)^{-1}R^T\begin{bmatrix}V_1 & V_2\end{bmatrix}$

For implementation purposes, the local warp transform is implemented as two shears: A horizontal shear and vertical shear. The model matrix H is then decomposed as follows:

$\begin{bmatrix}\color{orange}{h_{11}} & \color{orange}{h_{12}} \\ \color{orange}{h_{21}} & \color{orange}{h_{22}} \end{bmatrix} = \begin{bmatrix}1 & 0 \\ \gamma & 1+ \Delta \end{bmatrix}\begin{bmatrix}1+\alpha & \beta \\ 0 & 1 \end{bmatrix}$

where $\alpha,\beta,\Delta,\gamma$ are shear model parameters. The Vertical shear is given by the following model:

$\begin{bmatrix}x_r \\ y_r\end{bmatrix} = \begin{bmatrix}1 & 0 \\ \gamma & 1+ \Delta \end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}$

whereas the horizontal shear is given by,
$\begin{bmatrix}x_r \\ y_r\end{bmatrix} = \begin{bmatrix}1 + \alpha & \beta \\ 0 & 1 \end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}$

The combined transform is given by: $\begin{bmatrix}x_r \\ y_r\end{bmatrix} = \begin{bmatrix}1 & 0 \\ \gamma & 1+ \Delta \end{bmatrix}\begin{bmatrix}1+\alpha & \beta \\ 0 & 1 \end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}$

The shear parameters $\alpha,\beta,\Delta,\gamma$ are determined based on the parameters $\mathbf{h_{11},h_{12},h_{21}}$ and $\mathbf{h_{22}}$. Subpel displacements that results from the application of the horizontal and vertical shears are evaluated using 8-tap interpolation filters with $1/64^{th}$ pel precision.

The final warped motion model is applied on an 8x8 basis in the reference frame. The predicted block is constructed by assembling the 8x8 predicted warped blocks from the reference picture.

Figure 2. The horizontal, vertical, and combined shears respectively.

At the decoder side, the affine transform parameters are derived at the block-level using as input the motion vectors of the current and neighboring blocks.

2. Implementation of the algorithm

Control tokens/flags:

LW can be enabled/disabled at the sequence and the picture level as indicated in Table 1.

Table 1. Control tokens/flags associated with the LW feature.

Flag	Level (sequence/Picture)	Description
enable_warped_motion	Sequence	Encoder configuration parameter to allow/disallow LW in the encoding process for the whole sequence.
allow_warped_motion	Picture	Allow/disable LW at the picture level
wm_ctrls	Super-block	Control the number of LW candidates to be considered in the mode decision.

Details of the implementation

Figure 3 below summarizes the data flow of the LW implementation.

Figure 3. Data flow for the LW feature.

As with other prediction mode candidates in the encoder, candidates for the LW mode are first injected into MD and then processed through several MD stages of RD optimization. A high-level diagram of the function calls relevant to the two main LW functions, namely inject_inter_candidates and warped_motion_prediction is given in Figure 4 below.

Figure 4. Function calls relevant to the two main LW functions highlighted in blue.

The two main steps involved in the LW processing in MD, namely the injection of the LW candidates and the generation of the LW predictions are outlined in the following.

Step 1: Injection of the LW candidates.

The injection is performed by the function inject_inter_candidates. A diagram of the relevant function calls is given in Figure 5.

Figure 5. Continuation of Figure 3 with the function calls related to the injection of LW candidates.

1. Check if the current block has overlappable blocks above and/or to the left of the current block (has_overlappable_candidates). Overlappable blocks are adjacent blocks above or to the left of the current block that are inter blocks with width >= 8 and height >= 8.

2. Inject warped candidate (function inject_warped_motion_candidates) if the current block is such that width >= 8 and height >= 8 and warped_motion_injection is set.

   1. Get an MV. The MV would be from List 0 and could correspond to NEAREST MV, NEAR MV or NEW MV.

   2. Compute warped parameters (function warped_motion_parameters)

      1. Get warp samples

         1. Get MVs from overlappable neighboring blocks in the causal neighborhood, i.e. top and left of the current block. (wm_find_samples)

         2. Generate the list of warp samples, i.e., selection of samples (select_samples). To perform the selection of samples, the difference between the MV for the current block and the MV of the neighboring block is computed. The sum of the absolute values of the x and y components of the difference are compared to a threshold. Neighboring blocks that result in a large sum are not considered. Stop if number of samples in the list is small, since the estimated warp motion parameters would be unreliable.

      2. Warp parameters estimation (function svt_find_projection)

         1. Generate the warp motion parameters with the warp samples using the least squares fit (find_affine_int). Stop if parameters don’t fit threshold criteria.

         2. Generate warp variables alpha, beta, gamma and delta for the two shearing operations (i.e., horizontal and vertical, which combined make the full affine transformation). (svt_get_shear_params). Stop if the shear parameters are not valid (is_affine_shear_allowed).

   3. If not discarded, the LW candidate is added to the RD candidate list.

Step 2: Evaluation of the LW candidates in MD

The generation of the LW predictions in MD is performed using the function warped\_motion\_prediction. A diagram of the associated function call is shown in Figure 6 below.

Figure 6. Continuation of Figure 4 with the function calls related to the evaluation of the LW predictions in MD.

The steps involved in the generation and evaluation of the predictions are outlined below.

1. Generate warped motion predicted samples for each plane (plane_warped_motion_prediction)

   1. plane_warped_motion_prediction: Generates the luma and chroma warped luma predictions. The chroma predictions are generated for blocks that are 16x16 or larger.

      1. av1_dist_wtd_comp_weight_assign: Returns forward offset and backward offset for the case of compound reference candidates and where the inter-inter compound prediction mode is COMPOUND_DISTWTD. The forward offset and backward offset are used as weights in the generation of the final prediction.

      2. av1_make_masked_warp_inter_predictor: Called only in the case of compound reference candidate where the inter-inter compound type is COMPOUND_WEDGE or COMPOUND_DIFFWTD. Generates the predictions for both of those two compound types. The first step is to build the mask for the case of the COMPOUND_DIFFWTD inter-inter compound type using the function av1_build_compound_diffwtd_mask_d16. The next step is to generate the predictions using the function build_masked_compound_no_round as follows:

         1. The function av1_get_compound_type_mask is called and returns the mask for either the case of COMPOUND_DIFFWTD or for the case of COMPOUND_WEDGE. The function av1_get_contiguous_soft_mask returns the mask for the case of COMPOUND_WEDGE. For the case of COMPOUND_DIFFWTD, the mask is computed in the step above.

         2. The function aom_highbd_blend_a64_d16_mask/aom_lowbd_blend_a64_d16_mask is the called to perform the blending of the two inter predictions using the generated mask.

      3. svt_av1_warp_plane is invoked in the case of BIPRED where inter-inter compound type is COMPOUND_DISTWTD. In this case the function highbd_warp_plane / warp_plane is called and in turn calls the function svt_av1_highbd_warp_affine / svt_av1_warp_affine. The latter applies the affine transform and generates the warped motion prediction using the forward offset and backward offset weights associated with the COMPOUND_DISTWTD mode. This last step is performed at the level of 8x8 blocks, until the prediction for the entire block is generated.

   2. chroma_plane_warped_motion_prediction_sub8x8: Generates chroma warped motion predictions for blocks that are smaller than 16x16. The function av1_dist_wtd_comp_weight_assign is first called to generate the mask for the COMPOUND_DISTWTD case. The appropriate function in the function array convolve[][][] / convolveHbd[][][] is then called to generate the prediction using the forward offset and the backward offset weights.

2. Compute RD for the LW prediction. Rate includes the signaling of the syntax element motion_mode

Step 3: Generate the final warped motion predictions in the encode pass. The main relevant function is warped_motion_prediction which is described above.

3. Optimization of the algorithm

The injection of the LW motion candidates is performed if the following is true: allow_warped_motion is set AND the block has overlappable candidates AND bwidth >= 8 AND bheight >= 8 AND enable flag (in the LW controls structure) is set to 1.

The injection of LW candidates is not allowed for PD_PASS_0.

In mode decision, the picture-level flag wm_level controls the complexity-quality tradeoffs associated with the LW feature. The flag is set is set in signal_derivation_mode_decision_config_kernel_oq and control the LW optimization signals listed in Table 2 below.

The wm_level is set to zero for Intra pictures or when error_resilient_mode is enabled or when frame_super-resolution is enabled.

Table 2. Optimization signals associated with the LW feature.

Signal	Level	Description
enabled	Super-block	Allow/disallow the injection of LW candidates
use_wm_for_mvp	Super-block	Allow/disallow the injection of MVP-based LW candidates
num_new_mv_refinement	Super-block	Define the number of refinement positions around the NEW_MVs [0..12]

4. Signaling

The configuration flag enable_local_warp_flag controls the encoder use of LW at the sequence level. At the frame level, the use of LW is controlled by allow_warped_motion. At the block level, the use of LW is signaled by the syntax element motion_mode, which indicates the type of motion for a block: simple translation, OBMC, or warped motion.

Notes

The feature settings that are described in this document were compiled at v1.3.0 of the code and may not reflect the current status of the code. The description in this document represents an example showing how features would interact with the SVT architecture. For the most up-to-date settings, it's recommended to review the section of the code implementing this feature.

Reference

[1] Sarah Parker, Yue Chen, David Barker, Peter de Rivaz, Debargha Mukherjee, “Global and Locally Adaptive Warped Motion Compensation in Video Compression,” IEEE International Conference on Image Processing (ICIP), pp. 275-279, 2017.

[2] Jingning Han, Bohan Li, Debargha Mukherjee, Ching-Han Chiang, Adrian Grange, Cheng Chen, Hui Su, Sarah Parker, Sai Deng, Urvang Joshi, Yue Chen, Yunqing Wang, Paul Wilkins, Yaowu Xu, James Bankoski, “A Technical Overview of AV1,” Proceedings of the IEEE, vol. 109, no. 9, pp. 1435-1462, Sept. 2021.