#version 450 core
-in vec2 tc;
-out uvec4 equation;
+in vec3 tc0, tc_left0, tc_down0;
+in vec3 tc1, tc_left1, tc_down1;
+in float line_offset;
+out uvec4 equation_red, equation_black;
+
+uniform sampler2DArray I_x_y_tex, I_t_tex;
+uniform sampler2DArray diff_flow_tex, base_flow_tex;
+uniform sampler2DArray beta_0_tex;
+uniform sampler2DArray diffusivity_tex;
+
+// Relative weighting of intensity term.
+uniform float delta;
+
+// Relative weighting of gradient term.
+uniform float gamma;
+
+uniform bool zero_diff_flow;
+
+// Similar to packHalf2x16, but the two values share exponent, and are stored
+// as 12-bit fixed point numbers multiplied by that exponent (the leading one
+// can't be implicit in this kind of format). This allows us to store a much
+// greater range of numbers (8-bit, ie., full fp32 range), and also gives us an
+// extra mantissa bit. (Well, ostensibly two, but because the numbers have to
+// be stored denormalized, we only really gain one.)
+//
+// The price we pay is that if the numbers are of very different magnitudes,
+// the smaller number gets less precision.
+uint pack_floats_shared(float a, float b)
+{
+ float greatest = max(abs(a), abs(b));
+
+ // Find the exponent, increase it by one, and negate it.
+ // E.g., if the nonbiased exponent is 3, the number is between
+ // 2^3 and 2^4, so our normalization factor to get within -1..1
+ // is going to be 2^-4.
+ //
+ // exponent -= 127;
+ // exponent = -(exponent + 1);
+ // exponent += 127;
+ //
+ // is the same as
+ //
+ // exponent = 252 - exponent;
+ uint e = floatBitsToUint(greatest) & 0x7f800000u;
+ float normalizer = uintBitsToFloat((252 << 23) - e);
-uniform sampler2D I_x_y_tex, I_t_tex;
-uniform sampler2D diff_flow_tex, flow_tex;
-uniform sampler2D beta_0_tex;
-uniform sampler2D smoothness_x_tex, smoothness_y_tex;
+ // The exponent is the same range as fp32, so just copy it
+ // verbatim, shifted up to where the sign bit used to be.
+ e <<= 1;
-// TODO: Consider a specialized version for the case where we know that du = dv = 0,
-// since we run so few iterations.
+ // Quantize to 12 bits.
+ uint qa = uint(int(round(a * (normalizer * 2047.0))));
+ uint qb = uint(int(round(b * (normalizer * 2047.0))));
-// The base flow needs to be normalized.
-// TODO: Should we perhaps reduce this to a separate two-component
-// texture when calculating the derivatives?
-vec2 normalize_flow(vec3 flow)
-{
- return flow.xy / flow.z;
+ return (qa & 0xfffu) | ((qb & 0xfffu) << 12) | e;
}
-// This must be a macro, since the offset needs to be a constant expression.
-#define get_flow(x_offs, y_offs) \
- (normalize_flow(textureOffset(flow_tex, tc, ivec2((x_offs), (y_offs))).xyz) + \
- textureOffset(diff_flow_tex, tc, ivec2((x_offs), (y_offs))).xy)
+float zero_if_outside_border(vec4 val)
+{
+ if (val.w < 1.0f) {
+ // We hit the border (or more like half-way to it), so zero smoothness.
+ return 0.0f;
+ } else {
+ return val.x;
+ }
+}
-void main()
+uvec4 compute_equation(vec3 tc, vec3 tc_left, vec3 tc_down)
{
// Read the flow (on top of the u0/v0 flow).
- vec2 diff_flow = texture(diff_flow_tex, tc).xy;
- float du = diff_flow.x; // FIXME: convert to pixels?
- float dv = diff_flow.y;
+ float du, dv;
+ if (zero_diff_flow) {
+ du = dv = 0.0f;
+ } else {
+ vec2 diff_flow = texture(diff_flow_tex, tc).xy;
+ du = diff_flow.x;
+ dv = diff_flow.y;
+ }
// Read the first derivatives.
vec2 I_x_y = texture(I_x_y_tex, tc).xy;
float I_y = I_x_y.y;
float I_t = texture(I_t_tex, tc).x;
- // E_I term. Note that we don't square β_0, in line with DeepFlow,
- // even though it's probably an error.
- //
- // TODO: Evaluate squaring β_0.
- // FIXME: Should the penalizer be adjusted for 0..1 intensity range instead of 0..255?
- // TODO: Multiply by some alpha.
+ // E_I term. Note that we don't square β_0, in line with DeepFlow;
+ // it's probably an error (see variational_refinement.txt),
+ // but squaring it seems to give worse results.
float beta_0 = texture(beta_0_tex, tc).x;
- float k1 = beta_0 * inversesqrt(beta_0 * (I_x * du + I_y * dv + I_t) * (I_x * du + I_y * dv + I_t) + 1e-6);
+ 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);
float A11 = k1 * I_x * I_x;
float A12 = k1 * I_x * I_y;
float A22 = k1 * I_y * I_y;
- float b1 = -k1 * I_t;
- float b2 = -k1 * I_t;
+ float b1 = -k1 * I_t * I_x;
+ float b2 = -k1 * I_t * I_y;
// Compute the second derivatives. First I_xx and I_xy.
vec2 I_x_y_m2 = textureOffset(I_x_y_tex, tc, ivec2(-2, 0)).xy;
float I_xt = I_tx_ty.x;
float I_yt = I_tx_ty.y;
- // E_G term. Same TODOs as E_I. Same normalization as beta_0
- // (see derivatives.frag).
+ // E_G term. Same normalization as beta_0 (see derivatives.frag).
float beta_x = 1.0 / (I_xx * I_xx + I_xy * I_xy + 1e-7);
float beta_y = 1.0 / (I_xy * I_xy + I_yy * I_yy + 1e-7);
- float k2 = inversesqrt(
+ float k2 = gamma * inversesqrt(
beta_x * (I_xx * du + I_xy * dv + I_xt) * (I_xx * du + I_xy * dv + I_xt) +
beta_y * (I_xy * du + I_yy * dv + I_yt) * (I_xy * du + I_yy * dv + I_yt) +
1e-6);
b2 -= k_x * I_xy * I_xt + k_y * I_yy * I_yt;
// E_S term, sans the part on the right-hand side that deals with
- // the neighboring pixels.
- // TODO: Multiply by some gamma.
- float smooth_l = textureOffset(smoothness_x_tex, tc, ivec2(-1, 0)).x;
- float smooth_r = texture(smoothness_x_tex, tc).x;
- float smooth_d = textureOffset(smoothness_y_tex, tc, ivec2( 0, -1)).x;
- float smooth_u = texture(smoothness_y_tex, tc).x;
- A11 -= smooth_l + smooth_r + smooth_d + smooth_u;
- A22 -= smooth_l + smooth_r + smooth_d + smooth_u;
-
- // Laplacian of (u0 + du, v0 + dv), sans the central term.
+ // the neighboring pixels. The gamma is multiplied in in smoothness.frag.
+ //
+ // Note that we sample in-between two texels, which gives us the 0.5 *
+ // (x[-1] + x[0]) part for free. If one of the texels is a border
+ // texel, it will have zero alpha, and zero_if_outside_border() will
+ // set smoothness to zero.
+ float smooth_l = zero_if_outside_border(texture(diffusivity_tex, tc_left));
+ float smooth_r = zero_if_outside_border(textureOffset(diffusivity_tex, tc_left, ivec2(1, 0)));
+ float smooth_d = zero_if_outside_border(texture(diffusivity_tex, tc_down));
+ float smooth_u = zero_if_outside_border(textureOffset(diffusivity_tex, tc_down, ivec2(0, 1)));
+ A11 += smooth_l + smooth_r + smooth_d + smooth_u;
+ A22 += smooth_l + smooth_r + smooth_d + smooth_u;
+
+ // Laplacian of (u0, v0).
vec2 laplacian =
- smooth_l * get_flow(-1, 0) +
- smooth_r * get_flow(1, 0) +
- smooth_d * get_flow(0, -1) +
- smooth_u * get_flow(0, 1);
- b1 -= laplacian.x;
- b2 -= laplacian.y;
-
- // The central term of the Laplacian, for (u0, v0) only.
- // (The central term for (du, dv) is what we are solving for.)
- vec2 central = (smooth_l + smooth_r + smooth_d + smooth_u) * normalize_flow(texture(flow_tex, tc).xyz);
- b1 += central.x;
- b2 += central.y;
+ smooth_l * textureOffset(base_flow_tex, tc, ivec2(-1, 0)).xy +
+ smooth_r * textureOffset(base_flow_tex, tc, ivec2( 1, 0)).xy +
+ smooth_d * textureOffset(base_flow_tex, tc, ivec2( 0, -1)).xy +
+ smooth_u * textureOffset(base_flow_tex, tc, ivec2( 0, 1)).xy -
+ (smooth_l + smooth_r + smooth_d + smooth_u) * texture(base_flow_tex, tc).xy;
+ b1 += laplacian.x;
+ b2 += laplacian.y;
// Encode the equation down into four uint32s.
- equation.x = floatBitsToUint(1.0 / A11);
- equation.y = floatBitsToUint(A12);
- equation.z = floatBitsToUint(1.0 / A22);
- equation.w = packHalf2x16(vec2(b1, b2));
+ uvec4 ret;
+ ret.x = floatBitsToUint(1.0 / A11);
+ ret.y = floatBitsToUint(A12);
+ ret.z = floatBitsToUint(1.0 / A22);
+ ret.w = pack_floats_shared(b1, b2);
+ return ret;
+}
+
+void main()
+{
+ uvec4 eq0 = compute_equation(tc0, tc_left0, tc_down0);
+ uvec4 eq1 = compute_equation(tc1, tc_left1, tc_down1);
+
+ if ((int(round(line_offset)) & 1) == 1) {
+ // Odd line, so the right value is red.
+ equation_red = eq1;
+ equation_black = eq0;
+ } else {
+ equation_red = eq0;
+ equation_black = eq1;
+ }
}
projects / nageru / blobdiff