Make combine_two_pixels() handle the fact that the GPU has limited subpixel interpola...

[movit] / util.cpp

diff --git a/util.cpp b/util.cpp
index c6517c90fbe8af07733463fa9d41d0831a0a73f0..eeea198a4a074fa357311356d3157e7d00f15d36 100644 (file)
--- a/util.cpp
+++ b/util.cpp
@@ -5,6 +5,7 @@
 #include <math.h>
 #include "util.h"
 #include "opengl.h"
+#include "init.h"
 
 void hsv2rgb(float h, float s, float v, float *r, float *g, float *b)
 {
@@ -125,16 +126,44 @@ std::string output_glsl_mat3(const std::string &name, const Eigen::Matrix3d &m)
        return buf;
 }
 
-void combine_two_samples(float w1, float w2, float *offset, float *total_weight)
+void combine_two_samples(float w1, float w2, float *offset, float *total_weight, float *sum_sq_error)
 {
+       assert(movit_initialized);
        assert(w1 * w2 >= 0.0f);  // Should not have differing signs.
+       float z;  // Just a shorter name for offset.
        if (fabs(w1 + w2) < 1e-6) {
-               *offset = 0.5f;
-               *total_weight = 0.0f;
+               z = 0.5f;
        } else {
-               *offset = w2 / (w1 + w2);
-               *total_weight = w1 + w2;
+               z = w2 / (w1 + w2);
        }
+
+       // Round to the minimum number of bits we have measured earlier.
+       // The card will do this for us anyway, but if we know what the real z
+       // is, we can pick a better total_weight below.
+       z = lrintf(z / movit_texel_subpixel_precision) * movit_texel_subpixel_precision;
+       
+       // Choose total weight w so that we minimize total squared error
+       // for the effective weights:
+       //
+       //   e = (w(1-z) - a)² + (wz - b)²
+       //
+       // Differentiating by w and setting equal to zero:
+       //
+       //   2(w(1-z) - a)(1-z) + 2(wz - b)z = 0
+       //   w(1-z)² - a(1-z) + wz² - bz = 0
+       //   w((1-z)² + z²) = a(1-z) + bz
+       //   w = (a(1-z) + bz) / ((1-z)² + z²)
+       //
+       // If z had infinite precision, this would simply reduce to w = w1 + w2.
+       *total_weight = (w1 * (1 - z) + w2 * z) / (z * z + (1 - z) * (1 - z));
+       *offset = z;
+
+       if (sum_sq_error != NULL) {
+               float err1 = *total_weight * (1 - z) - w1;
+               float err2 = *total_weight * z - w2;
+               *sum_sq_error = err1 * err1 + err2 * err2;
+       }
+
        assert(*offset >= 0.0f);
        assert(*offset <= 1.0f);
 }