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# Subpel Interpolation in the Open-loop Motion Estimation appendix ## 1. Description of the algorithm The open loop motion estimation (ME) uses source input pictures as reference pictures and provides motion vectors with up to quarter-pel precision. The luminance samples at the half-pel positions are generated first by applying symmetric 4-tap filter F1 = {-4, 36, 36, -4} on the integer luminance samples. The values of the half-pel samples are generated for the whole input search region and stored in 3 different buffers. Then, the luminance samples at the quarter-pel positions are generated using a bilinear filter F2 = {1,1} that is applied on the full-pel luminance samples and the already computed half-pel luminance samples. In Figure 1 below, A00, A10, A01 and A11 represent the luminance samples at the integer positions; b, h and j are the luminance samples at the half-pel positions and a, c, d, e, f, g, i, k, n, p, q and r are the luminance samples at the quarter-pel positions.  ##### Figure 1. Fractional positions. Table 1 below summarizes the filters used to generate the luminance samples at the half-pel positions. ##### Table 1. Interpolation filters used in the generation of the half-pel positions in ME. | **Position** | **Frac-pos Y** | **Frac-pos X** | **Horizontal filter** | **Vertical filter** | | ------------ | -------------- | -------------- | --------------------- | ------------------- | | **b** | 0 | 2 | F1 | \- | | **h** | 2 | 0 | \- | F1 | | **j** | 2 | 2 | F1 | F1 | Table 2 below summarizes the filters used to generate the luminance samples at the quarter-pel positions. ##### 2. Interpolation filters used in the generation of the quarter-pel positions in ME. | **Position** | **Frac-pos Y** | **Frac-pos X** | **Filter** | **Interpolated sample value** | | -------------| -------------- | -------------- | ------------ | ----------------------------- | | **a** | 0 | 1 | F2 | A00 + b | | **c** | 0 | 3 | F2 | b + A10 | | **d** | 1 | 0 | F2 | A00 + h | | **e** | 1 | 1 | F2 | h + b | | **f** | 1 | 2 | F2 | b + j | | **g** | 1 | 3 | F2 | b + h' | | **i** | 2 | 1 | F2 | h + j | | **k** | 2 | 3 | F2 | j + h' | | **n** | 3 | 0 | F2 | h + A01 | | **p** | 3 | 1 | F2 | h + b' | | **q** | 3 | 2 | F2 | j + b' | | **r** | 3 | 3 | F2 | h' + b' | ## 2. Implementation of the algorithm The sub-pel search in motion estimation is invoked after the full-pel search is completed and the best integer position is determined. The half-pel/quarter-pel search is a refinement stage around the best selected position in the previous search stage. This refinement area is configurable depending on the desired quality/complexity tradeoff. For example, in Figure 2, a first tier of half-pel positions around the best full-pel position are checked and then a second and third tier of half-pel positions can be also checked. Similarly, during the quarter-pel refinement, various tiers of quarter-pel refinement positions can be checked. The enabling of the multi-tier refinement is controlled by the half\_pel\_mode flag for half-pel refinement and by the quarter\_pel\_mode flag for quarter-pel refinement. Moreover, the number of tiers to be considered in the refinement is determined by the H\_PEL\_SEARCH\_WIND and the Q\_PEL\_SEARCH\_WIND macros for half-pel and quarter-pel refinements, respectively.  ##### Figure 2. Subpel search refinement positions. The description of the half-pel and quarter-pel modes is provided in Table 3 and Table 4, respectively. The half-pel and quarter-pel modes for the different encoder presets are summarized in Table 5. ##### Table 3. half\_pel\_mode settings and description. | **half\_pel\_mode** | **Description** | | ----------------------- | ------------------------------- | | 0 (EX\_HP\_MODE) | Exhaustive 1/2-pel search mode. | | 1 (REFINMENT\_HP\_MODE) | Refinement 1/2-pel search mode. | ##### Table 4. quarter\_pel\_mode settings and description. | **quarter\_pel\_mode** | **Description** | | ----------------------- | ------------------------------- | | 0 ( EX\_QP\_MODE) | Exhaustive 1/4-pel search mode | | 1 (REFINMENT\_QP\_MODE) | Refinement 1/4-pel search mode. | ##### Table 5. Half-pel and quarter-pel search modes as a function of the encoder preset. | **Encoder Preset** | **half\_pel\_mode** | **quarter\_pel\_mode** | | ------------------ | ----------------------- | ----------------------- | | 0 | 0 (EX\_HP\_MODE) | 1 (REFINMENT\_QP\_MODE) | | 1 to 8 | 1 (REFINMENT\_HP\_MODE) | 1 (REFINMENT\_QP\_MODE) | ## Notes The feature settings that are described in this document were compiled at v0.8.3 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.
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