6 uniform sampler2D I_x_y_tex, I_t_tex;
7 uniform sampler2D diff_flow_tex, base_flow_tex;
8 uniform sampler2D beta_0_tex;
9 uniform sampler2D smoothness_x_tex, smoothness_y_tex;
11 // Relative weighting of intensity term.
14 // Relative weighting of gradient term.
17 uniform bool zero_diff_flow;
19 // Similar to packHalf2x16, but the two values share exponent, and are stored
20 // as 12-bit fixed point numbers multiplied by that exponent (the leading one
21 // can't be implicit in this kind of format). This allows us to store a much
22 // greater range of numbers (8-bit, ie., full fp32 range), and also gives us an
23 // extra mantissa bit. (Well, ostensibly two, but because the numbers have to
24 // be stored denormalized, we only really gain one.)
26 // The price we pay is that if the numbers are of very different magnitudes,
27 // the smaller number gets less precision.
28 uint pack_floats_shared(float a, float b)
30 float greatest = max(abs(a), abs(b));
32 // Find the exponent, increase it by one, and negate it.
33 // E.g., if the nonbiased exponent is 3, the number is between
34 // 2^3 and 2^4, so our normalization factor to get within -1..1
35 // is going to be 2^-4.
38 // exponent = -(exponent + 1);
43 // exponent = 252 - exponent;
44 uint e = floatBitsToUint(greatest) & 0x7f800000u;
45 float normalizer = uintBitsToFloat((252 << 23) - e);
47 // The exponent is the same range as fp32, so just copy it
48 // verbatim, shifted up to where the sign bit used to be.
51 // Quantize to 12 bits.
52 uint qa = uint(int(round(a * (normalizer * 2047.0))));
53 uint qb = uint(int(round(b * (normalizer * 2047.0))));
55 return (qa & 0xfffu) | ((qb & 0xfffu) << 12) | e;
60 // Read the flow (on top of the u0/v0 flow).
65 vec2 diff_flow = texture(diff_flow_tex, tc).xy;
70 // Read the first derivatives.
71 vec2 I_x_y = texture(I_x_y_tex, tc).xy;
74 float I_t = texture(I_t_tex, tc).x;
76 // E_I term. Note that we don't square β_0, in line with DeepFlow;
77 // it's probably an error (see variational_refinement.txt),
78 // but squaring it seems to give worse results.
79 float beta_0 = texture(beta_0_tex, tc).x;
80 float k1 = delta * beta_0 * inversesqrt(beta_0 * (I_x * du + I_y * dv + I_t) * (I_x * du + I_y * dv + I_t) + 1e-6);
81 float A11 = k1 * I_x * I_x;
82 float A12 = k1 * I_x * I_y;
83 float A22 = k1 * I_y * I_y;
84 float b1 = -k1 * I_t * I_x;
85 float b2 = -k1 * I_t * I_y;
87 // Compute the second derivatives. First I_xx and I_xy.
88 vec2 I_x_y_m2 = textureOffset(I_x_y_tex, tc, ivec2(-2, 0)).xy;
89 vec2 I_x_y_m1 = textureOffset(I_x_y_tex, tc, ivec2(-1, 0)).xy;
90 vec2 I_x_y_p1 = textureOffset(I_x_y_tex, tc, ivec2( 1, 0)).xy;
91 vec2 I_x_y_p2 = textureOffset(I_x_y_tex, tc, ivec2( 2, 0)).xy;
92 vec2 I_xx_yx = (I_x_y_p1 - I_x_y_m1) * (2.0/3.0) + (I_x_y_m2 - I_x_y_p2) * (1.0/12.0);
93 float I_xx = I_xx_yx.x;
94 float I_xy = I_xx_yx.y;
96 // And now I_yy; I_yx = I_xy, bar rounding differences, so we don't
97 // bother computing it. We still have to sample the x component,
98 // though, but we can throw it away immediately.
99 float I_y_m2 = textureOffset(I_x_y_tex, tc, ivec2(0, -2)).y;
100 float I_y_m1 = textureOffset(I_x_y_tex, tc, ivec2(0, -1)).y;
101 float I_y_p1 = textureOffset(I_x_y_tex, tc, ivec2(0, 1)).y;
102 float I_y_p2 = textureOffset(I_x_y_tex, tc, ivec2(0, 2)).y;
103 float I_yy = (I_y_p1 - I_y_m1) * (2.0/3.0) + (I_y_m2 - I_y_p2) * (1.0/12.0);
105 // Finally I_xt and I_yt. (We compute these as I_tx and I_yt.)
106 vec2 I_t_m2 = textureOffset(I_t_tex, tc, ivec2(-2, 0)).xy;
107 vec2 I_t_m1 = textureOffset(I_t_tex, tc, ivec2(-1, 0)).xy;
108 vec2 I_t_p1 = textureOffset(I_t_tex, tc, ivec2( 1, 0)).xy;
109 vec2 I_t_p2 = textureOffset(I_t_tex, tc, ivec2( 2, 0)).xy;
110 vec2 I_tx_ty = (I_t_p1 - I_t_m1) * (2.0/3.0) + (I_t_m2 - I_t_p2) * (1.0/12.0);
111 float I_xt = I_tx_ty.x;
112 float I_yt = I_tx_ty.y;
114 // E_G term. Same normalization as beta_0 (see derivatives.frag).
115 float beta_x = 1.0 / (I_xx * I_xx + I_xy * I_xy + 1e-7);
116 float beta_y = 1.0 / (I_xy * I_xy + I_yy * I_yy + 1e-7);
117 float k2 = gamma * inversesqrt(
118 beta_x * (I_xx * du + I_xy * dv + I_xt) * (I_xx * du + I_xy * dv + I_xt) +
119 beta_y * (I_xy * du + I_yy * dv + I_yt) * (I_xy * du + I_yy * dv + I_yt) +
121 float k_x = k2 * beta_x;
122 float k_y = k2 * beta_y;
123 A11 += k_x * I_xx * I_xx + k_y * I_xy * I_xy;
124 A12 += k_x * I_xx * I_xy + k_y * I_xy * I_yy;
125 A22 += k_x * I_xy * I_xy + k_y * I_yy * I_yy;
126 b1 -= k_x * I_xx * I_xt + k_y * I_xy * I_yt;
127 b2 -= k_x * I_xy * I_xt + k_y * I_yy * I_yt;
129 // E_S term, sans the part on the right-hand side that deals with
130 // the neighboring pixels. The gamma is multiplied in in smoothness.frag.
131 float smooth_l = textureOffset(smoothness_x_tex, tc, ivec2(-1, 0)).x;
132 float smooth_r = texture(smoothness_x_tex, tc).x;
133 float smooth_d = textureOffset(smoothness_y_tex, tc, ivec2( 0, -1)).x;
134 float smooth_u = texture(smoothness_y_tex, tc).x;
135 A11 += smooth_l + smooth_r + smooth_d + smooth_u;
136 A22 += smooth_l + smooth_r + smooth_d + smooth_u;
138 // Laplacian of (u0, v0).
140 smooth_l * textureOffset(base_flow_tex, tc, ivec2(-1, 0)).xy +
141 smooth_r * textureOffset(base_flow_tex, tc, ivec2( 1, 0)).xy +
142 smooth_d * textureOffset(base_flow_tex, tc, ivec2( 0, -1)).xy +
143 smooth_u * textureOffset(base_flow_tex, tc, ivec2( 0, 1)).xy -
144 (smooth_l + smooth_r + smooth_d + smooth_u) * texture(base_flow_tex, tc).xy;
148 // Encode the equation down into four uint32s.
149 equation.x = floatBitsToUint(1.0 / A11);
150 equation.y = floatBitsToUint(A12);
151 equation.z = floatBitsToUint(1.0 / A22);
152 equation.w = pack_floats_shared(b1, b2);