Appendix-Local-Warped-Motion.md

Local Warped Motion Compensation Appendix

1. Description of the algorithm

Warped motion modes are inter-prediction modes 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 local motion model parameters. The general motion model for local warped motion is given by

where and 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 and , i.e. the rest of the model parameters are not signaled in the bitstream.

To simplify the model estimation, and are assumed to represent the entries in the current block motion vector (MV in the Figure 1 below).

Let MV= . Then the above implies . The remaining parameters , and are estimated using a least squares approach.

To illustrate the estimation of the parameters and using a least squares approach, consider the 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.

In the following, assume the x and y coordinates are specified with reference to the top left corner of the yellow block. Let be the center of the current block, and the projection of (C) onto the reference frame using the motion vector MV for the current block. According to the motion model:

For block 6, define to be the center of block 6, and to be the projection of onto the reference frame using the mv for block 6. Assuming the same motion model as above, it follows that:

Taking the difference between the two equations above:

The local warp transformation defines how the vector relating and in the source frame is projected into the vector relating and in the reference frame.

= where

The vectors and are shown in purple in Figure 1. The steps above are then repeated for blocks 5 and 3. The least squares minimization problem is then broken into two estimation problems: One of the estimation problems is to determine the parameters and the other is to estimate the parameters such that

and where the matrices and are constructed from the data above. The solutions to the least squares estimation problems are then given as and

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:

where are shear model parameters. The Vertical shear is given by the following model:

whereas the horizontal shear is given by:

The combined transform is given by:

The shear parameters are determined based on the parameters and . Subpel displacements that results from the application of the horizontal and vertical shears are evaluated using 8-tap interpolation filters with pel precision.

The final warped motion model is applied on an 8x8 basis in the source 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 macros/flags:

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

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

Flag	Level (sequence/Picture)	Description
-local-warp	Config / Sequence	Encoder configuration parameter to enable/disable LW
allow_warped_motion	Picture	Enable/disable LW

Details of the implementation

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 3 below.

Figure 3. 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 4.

Figure 4. 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 eb_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). (eb_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 andidate 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 5 below.

Figure 5. Continuation of Figure 3 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. eb_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 eb_av1_highbd_warp_affine / eb_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 warped_motion_injection is set. The flag warped_motion_injection is set in signal_derivation_enc_dec_kernel_oq as shown in Table 2 below:

Table 2. warped_motion_injection as a function of encoder settings.

PD_PASS	warped_motion_injection
PD_PASS_0	0
PD_PASS_1	1
Otherwise	if sc_content_detected then 0, else 1

In mode decision, the picture-level flag allow_warped_motion is set in signal_derivation_mode_decision_config_kernel_oq as shown in Table 3 below.

Table 3. enable_wm setting as a function of encoder preset.

The final setting for allow_warped_motion is determined as follows: allow_warped_motion = enable_wm AND not KEY_FRAME AND not INTRA_ONLY_FRAME and not error_resilient_mode.

4. Signaling

The configuration flag enable_local_warp_flag controls the encoder use of LW at the sequence level. At 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.

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.