What is the definition of "Error surface" in HEVC

Question

I'm reading a paper about sub-pixel motion estimation optimization algorithm in HEVC; while all the proposed concepts are based on "Modeling the Error Surface" in the search range(search window)during algorithm;

Does anybody by any chance know the definition of "Error Surface" here?

And what I'm lookin for is definitely not this: Freeform surface modelling.

Thanks.

By the way, the paper's link is here.

Answer 1

The picture below (from the Geneva meeting in January this year) shows the

Integer samples (shaded blocks with upper-case letters) and fractional sample positions (un-shaded blocks with lower-case letters) for quarter sample luma interpolation

The following calculations are needed for the quarter-sample-interpolation:

a0,0 = ( ?A?3,0 + 4 * A?2,0 ? 10 * A?1,0 + 58 * A0,0 +   17 * A1,0 ? 5 * A2,0 + A3,0 )  >>  shift1  (8?292)
b0,0 = ( ?A?3,0 + 4 * A?2,0 ? 11 * A?1,0 + 40 * A0,0 +   40 * A1,0 ? 11 * A2,0 + 4 * A3,0 ? A4,0 )  >>  shift1  (8?293)
c0,0 = ( A?2,0 ? 5 * A?1,0 + 17 * A0,0 +     58 * A1,0 ? 10 * A2,0 + 4 * A3,0 ? A4,0 )  >>  shift1  (8?294)
d0,0 = ( ?A0,?3 + 4 * A0,?2 ? 10 * A0,?1 + 58 * A0,0 +   17 * A0,1 ? 5 * A0,2 + A0,3 )  >>  shift1  (8?295)
h0,0 = ( ?A0,?3 + 4 * A0,?2 ? 11 * A0,?1 + 40 * A0,0 +   40 * A0,1 ? 11 * A0,2 + 4 * A0,3 ? A0,4 )  >>  shift1  (8?296)
n0,0 = ( A0,?2 ? 5 * A0,?1 + 17 * A0,0 +     58 * A0,1 ? 10 * A0,2 + 4 * A0,3 ? A0,4 )  >>  shift1  (8?297)

–   The samples labelled e0,0, i0,0, p0,0, f0,0, j0,0, q0,0, g0,0, k0,0, and r0,0
    are derived by applying an 8-tap filter to the samples a0,i, b0,i and c0,i with
    i = ?3..4 in the vertical direction as follows:

e0,0 = ( ?a0,?3 + 4 * a0,?2 ? 10 * a0,?1 + 58 * a0,0 +   17 * a0,1 ? 5 * a0,2 + a0,3 )  >>  shift2  (8?298)
i0,0 = ( ?a0,?3 + 4 * a0,?2 ? 11 * a0,?1 + 40 * a0,0 +   40 * a0,1 ? 11 * a0,2 + 4 * a0,3 ? a0,4 )  >>  shift2  (8?299)
p0,0 = ( a0,?2 ? 5 * a0,?1 + 17 * a0,0 +     58 * a0,1 ? 10 * a0,2 + 4 * a0,3 ? a0,4 )  >>  shift2  (8?300)
f0,0 = ( ?b0,?3 + 4 * b0,?2 ? 10 * b0,?1 + 58 * b0,0 +   17 * b0,1 ? 5 * b0,2 + b0,3 )  >>  shift2  (8?301)
j0,0 = ( ?b0,?3 + 4 * b0,?2 ? 11 * b0,?1 + 40 * b0,0 +   40 * b0,1 ? 11 * b0,2 + 4 * b0,3 ? b0,4 )  >>  shift2  (8?302)
q0,0 = ( b0,?2 ? 5 * b0,?1 + 17 * b0,0 +     58 * b0,1 ? 10 * b0,2 + 4 * b0,3 ? b0,4 )  >>  shift2  (8?303)
g0,0 = ( ?c0,?3 + 4 * c0,?2 ? 10 * c0,?1 + 58 * c0,0 +   17 * c0,1 ? 5 * c0,2 + c0,3 )  >>  shift2  (8?304)
k0,0 = ( ?c0,?3 + 4 * c0,?2 ? 11 * c0,?1 + 40 * c0,0 +   40 * c0,1 ? 11 * c0,2 + 4 * c0,3 ? c0,4 )  >>  shift2  (8?305)
r0,0 = ( c0,?2 ? 5 * c0,?1 + 17 * c0,0 +     58 * c0,1 ? 10 * c0,2 + 4 * c0,3 ? c0,4 )  >>  shift2  (8?306)

Quite a mouthful as you can see...

The paper you are referring to error surface is probably the difference between the pixel-values calculated using the method proposed in the standard and the second-order-function proposed in the paper. Hope it helps :-)