Also calculate beta_0 when calculating derivatives.

diff --git a/derivatives.frag b/derivatives.frag
index e5e355700f56e1197d1ca3cd2326ae346d98a651..b10125ea13cd1e539360ecaab519e065cc6b85bb 100644 (file)
--- a/derivatives.frag
+++ b/derivatives.frag
@@ -2,6 +2,7 @@
 
 in vec2 tc;
 out vec2 derivatives;
+out float beta_0;
 
 uniform sampler2D tex;
 
@@ -19,4 +20,13 @@ void main()
 
        derivatives.x = (x_p1 - x_m1) * (2.0/3.0) + (x_m2 - x_p2) * (1.0/12.0);
        derivatives.y = (y_p1 - y_m1) * (2.0/3.0) + (y_m2 - y_p2) * (1.0/12.0);
+
+       // The nudge term in the square root in the DeepFlow paper is ζ² = 0.1² = 0.01.
+       // But this is assuming a 0..255 level. Given the nonlinearities in the expression
+       // where β_0 appears, there's no 100% equivalent way to adjust this
+       // constant that I can see, but taking it to (0.1/255)² ~= 1.53e-7 ~=
+       // 1e-7 ought to be good enough. I guess the basic idea is that it
+       // will only matter for near-zero derivatives anyway. I am a tiny
+       // bit worried about fp16 precision when storing these numbers, but OK.
+       beta_0 = 1.0 / (derivatives.x * derivatives.x + derivatives.y * derivatives.y + 1e-7);
 }

diff --git a/flow.cpp b/flow.cpp
index 39b6a74317f051df37b50a8e313fd67a53e257da..8250aa3a885e63c633988ad76c3015a142aa0767 100644 (file)
--- a/flow.cpp
+++ b/flow.cpp
@@ -469,10 +469,12 @@ void Prewarp::exec(GLuint tex0_view, GLuint tex1_view, GLuint flow_tex, GLuint I
 // The coefficients come from
 //
 //   https://en.wikipedia.org/wiki/Finite_difference_coefficient
+//
+// Also computes β_0, since it depends only on I_x and I_y.
 class Derivatives {
 public:
        Derivatives();
-       void exec(GLuint input_tex, GLuint output_tex, int level_width, int level_height);
+       void exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, int level_width, int level_height);
 
 private:
        GLuint derivatives_vs_obj;
@@ -501,7 +503,7 @@ Derivatives::Derivatives()
        uniform_tex = glGetUniformLocation(derivatives_program, "tex");
 }
 
-void Derivatives::exec(GLuint input_tex, GLuint output_tex, int level_width, int level_height)
+void Derivatives::exec(GLuint input_tex, GLuint I_x_y_tex, GLuint beta_0_tex, int level_width, int level_height)
 {
        glUseProgram(derivatives_program);
 
@@ -509,7 +511,10 @@ void Derivatives::exec(GLuint input_tex, GLuint output_tex, int level_width, int
 
        GLuint derivatives_fbo;  // TODO: cleanup
        glCreateFramebuffers(1, &derivatives_fbo);
-       glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT0, output_tex, 0);
+       GLenum bufs[] = { GL_COLOR_ATTACHMENT0, GL_COLOR_ATTACHMENT1 };
+       glNamedFramebufferDrawBuffers(derivatives_fbo, 2, bufs);
+       glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT0, I_x_y_tex, 0);
+       glNamedFramebufferTexture(derivatives_fbo, GL_COLOR_ATTACHMENT1, beta_0_tex, 0);
 
        glViewport(0, 0, level_width, level_height);
        glDisable(GL_BLEND);
@@ -643,17 +648,17 @@ int main(void)
                glTextureStorage2D(I_t_tex, 1, GL_R16F, level_width, level_height);
                prewarp.exec(tex0_view, tex1_view, dense_flow_tex, I_tex, I_t_tex, level_width, level_height);
 
-               // Derivatives of the images. We're only calculating first derivatives;
+               // Calculate I_x and I_y. We're only calculating first derivatives;
                // the others will be taken on-the-fly in order to sample from fewer
                // textures overall, since sampling from the L1 cache is cheap.
                // (TODO: Verify that this is indeed faster than making separate
                // double-derivative textures.)
-
-               // Calculate I_x and I_y.
-               GLuint I_x_y_tex;
+               GLuint I_x_y_tex, beta_0_tex;
                glCreateTextures(GL_TEXTURE_2D, 1, &I_x_y_tex);
+               glCreateTextures(GL_TEXTURE_2D, 1, &beta_0_tex);
                glTextureStorage2D(I_x_y_tex, 1, GL_RG16F, level_width, level_height);
-               derivatives.exec(I_tex, I_x_y_tex, level_width, level_height);
+               glTextureStorage2D(beta_0_tex, 1, GL_R16F, level_width, level_height);
+               derivatives.exec(I_tex, I_x_y_tex, beta_0_tex, level_width, level_height);
 
                prev_level_flow_tex = dense_flow_tex;
        }