

#### 15.2 Simple Filter                                      {#h-15-02}


Having described the overall procedure of, and pixels affected by, the loop filter, we turn our attention to the treatment of individual segments straddling edges. We begin by describing the simple filter, which, as the reader might guess, is somewhat simpler than the normal filter.

Note that the simple filter only applies to luma edges. Chroma edges are left unfiltered.

Roughly speaking, the idea of loop filtering is, within limits, to reduce the difference between pixels straddling an edge. Differences in excess of a threshold (associated to the `loop_filter_level`) are assumed to be "natural" and are unmodified; differences below the threshold are assumed to be artifacts of quantization and the (partially) separate coding of blocks, and are reduced via the procedures described below. While the `loop_filter_level` is in principle arbitrary, the levels chosen by a VP8 compressor tend to be correlated to quantization levels.

Most of the filtering arithmetic is done using 8-bit signed operands (having a range -128 to +127, inclusive), supplemented by 16-bit temporaries holding results of multiplies.

Sums and other temporaries need to be "clamped" to a valid signed 8-bit range:


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int8 c( int v)
{
    return (int8) (v < -128 ? -128 : (v < 128 ? v : 127));
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
{:lang="c"}


Since pixel values themselves are unsigned 8-bit numbers, we need to convert between signed and unsigned values:


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/* Convert pixel value (0 <= v <= 255) to an 8-bit signed
   number. */
int8 u2s( Pixel v) { return (int8) (v - 128);}

/* Clamp, then convert signed number back to pixel value. */
Pixel s2u( int v) { return (Pixel) ( c(v) + 128);}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
{:lang="c"}


Filtering is often predicated on absolute-value thresholds. The following function is the equivalent of the standard library function `abs`, whose prototype is found in the standard header file `stdlib.h`. For us, the argument `v` is always the difference between two pixels and lies in the range [[ -255 <= v <= +255 ]].


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int abs( int v) { return v < 0?  -v : v;}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
{:lang="c"}


An actual implementation would of course use inline functions or macros to accomplish these trivial procedures (which are used by both the normal and simple loop filters). An optimal implementation would probably express them in machine language, perhaps using SIMD vector instructions. On many SIMD processors, the saturation accomplished by the above clamping function is often folded into the arithmetic instructions themselves, obviating the explicit step taken here.

To simplify the specification of relative pixel positions, we use the word before to mean "immediately above" (for a vertical segment straddling a horizontal edge) or "immediately to the left of" (for a horizontal segment straddling a vertical edge) and the word after to mean "immediately below" or "immediately to the right of".

Given an edge, a segment, and a limit value, the simple loop filter computes a value based on the four pixels that straddle the edge (two either side). If that value is below a supplied limit, then, very roughly speaking, the two pixel values are brought closer to each other, "shaving off" something like a quarter of the difference. The same procedure is used for all segments straddling any type of edge, regardless of the nature (inter-macroblock, inter-subblock, luma, or chroma) of the edge; only the limit value depends on the edge-type.

The exact procedure (for a single segment) is as follows; the subroutine common_adjust is used by both the simple filter presented here and the normal filters discussed in [Section 15.3](#h-15-03).


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int8 common_adjust(
    int use_outer_taps,   /* filter is 2 or 4 taps wide */
    const Pixel *P1,    /* pixel before P0 */
    Pixel *P0,          /* pixel before edge */
    Pixel *Q0,          /* pixel after edge */
    const Pixel *Q1     /* pixel after Q0 */
) {
    cint8 p1 = u2s( *P1);   /* retrieve and convert all 4 pixels */
    cint8 p0 = u2s( *P0);
    cint8 q0 = u2s( *Q0);
    cint8 q1 = u2s( *Q1);

    /* Disregarding clamping, when "use_outer_taps" is false,
       "a" is 3*(q0-p0). Since we are about to divide "a" by
       8, in this case we end up multiplying the edge
       difference by 5/8.

       When "use_outer_taps" is true (as for the simple filter),
       "a" is p1 - 3*p0 + 3*q0 - q1, which can be thought of as
       a refinement of 2*(q0 - p0) and the adjustment is
       something like (q0 - p0)/4. */

    int8 a = c( ( use_outer_taps? c(p1 - q1) : 0 ) + 3*(q0 - p0) );

    /* b is used to balance the rounding of a/8 in the case where
       the "fractional" part "f" of a/8 is exactly 1/2. */

    cint8 b = (c(a + 3)) >> 3;

    /* Divide a by 8, rounding up when f >= 1/2.
       Although not strictly part of the "C" language,
       the right-shift is assumed to propagate the sign bit. */

    a = c( a + 4) >> 3;

    /* Subtract "a" from q0, "bringing it closer" to p0. */

    *Q0 = s2u( q0 - a);

    /* Add "a" (with adjustment "b") to p0, "bringing it closer"
       to q0.

       The clamp of "a+b", while present in the reference decoder,
       is superfluous; we have -16 <= a <= 15 at this point. */

    *P0 = s2u( p0 + b);

    return a;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
{:lang="c"}


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
void simple_segment(
    uint8 edge_limit,   /* do nothing if edge difference
                           exceeds limit */
    const Pixel *P1,    /* pixel before P0 */
    Pixel *P0,          /* pixel before edge */
    Pixel *Q0,          /* pixel after edge */
    const Pixel *Q1     /* pixel after Q0 */
) {
    if( (abs(*P0 - *Q0)*2 + abs(*P1-*Q1)/2) <= edge_limit))
        common_adjust( 1, P1, P0, Q0, Q1);   /* use outer taps */
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
{:lang="c"}


We make a couple of remarks about the rounding procedure above. When `b` is zero (that is, when the "fractional part" of `a` is not 1/2 ), we are (except for clamping) adding the same number to `p0` as we are subtracting from `q0`. This preserves the average value of `p0` and `q0` but the resulting difference between `p0` and `q0` is always even; in particular, the smallest non-zero gradation [[ +-1 ]] is not possible here.

When `b` is one, the value we add to `p0` (again except for clamping) is one less than the value we are subtracting from `q0`. In this case, the resulting difference is always odd (and the small gradation [[ +-1 ]] is possible) but the average value is reduced by 1/2, yielding, for instance, a very slight darkening in the luma plane. (In the very unlikely event of appreciable darkening after a large number of interframes, a compressor would of course eventually compensate for this in the selection of predictor and/or residue.)

The derivation of the `edge_limit` value used above, which depends on the `loop_filter_level` and `sharpness_level`, as well as the type of edge being processed, will be taken up after we describe the normal loop filtering algorithm below.