Import aom library

This is the reference implementation for the Alliance for Open Media's av1 video code.

The commit used was 4d668d7feb1f8abd809d1bca0418570a7f142a36.

1 files changed, 1210 insertions, 0 deletions

diff --git a/third_party/aom/av1/encoder/ransac.c b/third_party/aom/av1/encoder/ransac.c
new file mode 100644
index 000000000..5d5dd7572
--- /dev/null
+++ b/third_party/aom/av1/encoder/ransac.c
@@ -0,0 +1,1210 @@
+/*
+ * Copyright (c) 2016, Alliance for Open Media. All rights reserved
+ *
+ * This source code is subject to the terms of the BSD 2 Clause License and
+ * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
+ * was not distributed with this source code in the LICENSE file, you can
+ * obtain it at www.aomedia.org/license/software. If the Alliance for Open
+ * Media Patent License 1.0 was not distributed with this source code in the
+ * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
+ */
+#define _POSIX_C_SOURCE 200112L  // rand_r()
+#include <memory.h>
+#include <math.h>
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+
+#include "av1/encoder/ransac.h"
+
+#define MAX_MINPTS 4
+#define MAX_DEGENERATE_ITER 10
+#define MINPTS_MULTIPLIER 5
+
+#define INLIER_THRESHOLD 1.0
+#define MIN_TRIALS 20
+
+////////////////////////////////////////////////////////////////////////////////
+// ransac
+typedef int (*IsDegenerateFunc)(double *p);
+typedef void (*NormalizeFunc)(double *p, int np, double *T);
+typedef void (*DenormalizeFunc)(double *params, double *T1, double *T2);
+typedef int (*FindTransformationFunc)(int points, double *points1,
+                                      double *points2, double *params);
+typedef void (*ProjectPointsDoubleFunc)(double *mat, double *points,
+                                        double *proj, const int n,
+                                        const int stride_points,
+                                        const int stride_proj);
+
+static void project_points_double_translation(double *mat, double *points,
+                                              double *proj, const int n,
+                                              const int stride_points,
+                                              const int stride_proj) {
+  int i;
+  for (i = 0; i < n; ++i) {
+    const double x = *(points++), y = *(points++);
+    *(proj++) = x + mat[0];
+    *(proj++) = y + mat[1];
+    points += stride_points - 2;
+    proj += stride_proj - 2;
+  }
+}
+
+static void project_points_double_rotzoom(double *mat, double *points,
+                                          double *proj, const int n,
+                                          const int stride_points,
+                                          const int stride_proj) {
+  int i;
+  for (i = 0; i < n; ++i) {
+    const double x = *(points++), y = *(points++);
+    *(proj++) = mat[2] * x + mat[3] * y + mat[0];
+    *(proj++) = -mat[3] * x + mat[2] * y + mat[1];
+    points += stride_points - 2;
+    proj += stride_proj - 2;
+  }
+}
+
+static void project_points_double_affine(double *mat, double *points,
+                                         double *proj, const int n,
+                                         const int stride_points,
+                                         const int stride_proj) {
+  int i;
+  for (i = 0; i < n; ++i) {
+    const double x = *(points++), y = *(points++);
+    *(proj++) = mat[2] * x + mat[3] * y + mat[0];
+    *(proj++) = mat[4] * x + mat[5] * y + mat[1];
+    points += stride_points - 2;
+    proj += stride_proj - 2;
+  }
+}
+
+static void project_points_double_hortrapezoid(double *mat, double *points,
+                                               double *proj, const int n,
+                                               const int stride_points,
+                                               const int stride_proj) {
+  int i;
+  double x, y, Z, Z_inv;
+  for (i = 0; i < n; ++i) {
+    x = *(points++), y = *(points++);
+    Z_inv = mat[7] * y + 1;
+    assert(fabs(Z_inv) > 0.000001);
+    Z = 1. / Z_inv;
+    *(proj++) = (mat[2] * x + mat[3] * y + mat[0]) * Z;
+    *(proj++) = (mat[5] * y + mat[1]) * Z;
+    points += stride_points - 2;
+    proj += stride_proj - 2;
+  }
+}
+
+static void project_points_double_vertrapezoid(double *mat, double *points,
+                                               double *proj, const int n,
+                                               const int stride_points,
+                                               const int stride_proj) {
+  int i;
+  double x, y, Z, Z_inv;
+  for (i = 0; i < n; ++i) {
+    x = *(points++), y = *(points++);
+    Z_inv = mat[6] * x + 1;
+    assert(fabs(Z_inv) > 0.000001);
+    Z = 1. / Z_inv;
+    *(proj++) = (mat[2] * x + mat[0]) * Z;
+    *(proj++) = (mat[4] * x + mat[5] * y + mat[1]) * Z;
+    points += stride_points - 2;
+    proj += stride_proj - 2;
+  }
+}
+
+static void project_points_double_homography(double *mat, double *points,
+                                             double *proj, const int n,
+                                             const int stride_points,
+                                             const int stride_proj) {
+  int i;
+  double x, y, Z, Z_inv;
+  for (i = 0; i < n; ++i) {
+    x = *(points++), y = *(points++);
+    Z_inv = mat[6] * x + mat[7] * y + 1;
+    assert(fabs(Z_inv) > 0.000001);
+    Z = 1. / Z_inv;
+    *(proj++) = (mat[2] * x + mat[3] * y + mat[0]) * Z;
+    *(proj++) = (mat[4] * x + mat[5] * y + mat[1]) * Z;
+    points += stride_points - 2;
+    proj += stride_proj - 2;
+  }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// svdcmp
+// Adopted from Numerical Recipes in C
+
+static const double TINY_NEAR_ZERO = 1.0E-12;
+
+static INLINE double sign(double a, double b) {
+  return ((b) >= 0 ? fabs(a) : -fabs(a));
+}
+
+static INLINE double pythag(double a, double b) {
+  double ct;
+  const double absa = fabs(a);
+  const double absb = fabs(b);
+
+  if (absa > absb) {
+    ct = absb / absa;
+    return absa * sqrt(1.0 + ct * ct);
+  } else {
+    ct = absa / absb;
+    return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct);
+  }
+}
+
+static void multiply_mat(const double *m1, const double *m2, double *res,
+                         const int m1_rows, const int inner_dim,
+                         const int m2_cols) {
+  double sum;
+
+  int row, col, inner;
+  for (row = 0; row < m1_rows; ++row) {
+    for (col = 0; col < m2_cols; ++col) {
+      sum = 0;
+      for (inner = 0; inner < inner_dim; ++inner)
+        sum += m1[row * inner_dim + inner] * m2[inner * m2_cols + col];
+      *(res++) = sum;
+    }
+  }
+}
+
+static int svdcmp(double **u, int m, int n, double w[], double **v) {
+  const int max_its = 30;
+  int flag, i, its, j, jj, k, l, nm;
+  double anorm, c, f, g, h, s, scale, x, y, z;
+  double *rv1 = (double *)aom_malloc(sizeof(*rv1) * (n + 1));
+  g = scale = anorm = 0.0;
+  for (i = 0; i < n; i++) {
+    l = i + 1;
+    rv1[i] = scale * g;
+    g = s = scale = 0.0;
+    if (i < m) {
+      for (k = i; k < m; k++) scale += fabs(u[k][i]);
+      if (scale != 0.) {
+        for (k = i; k < m; k++) {
+          u[k][i] /= scale;
+          s += u[k][i] * u[k][i];
+        }
+        f = u[i][i];
+        g = -sign(sqrt(s), f);
+        h = f * g - s;
+        u[i][i] = f - g;
+        for (j = l; j < n; j++) {
+          for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j];
+          f = s / h;
+          for (k = i; k < m; k++) u[k][j] += f * u[k][i];
+        }
+        for (k = i; k < m; k++) u[k][i] *= scale;
+      }
+    }
+    w[i] = scale * g;
+    g = s = scale = 0.0;
+    if (i < m && i != n - 1) {
+      for (k = l; k < n; k++) scale += fabs(u[i][k]);
+      if (scale != 0.) {
+        for (k = l; k < n; k++) {
+          u[i][k] /= scale;
+          s += u[i][k] * u[i][k];
+        }
+        f = u[i][l];
+        g = -sign(sqrt(s), f);
+        h = f * g - s;
+        u[i][l] = f - g;
+        for (k = l; k < n; k++) rv1[k] = u[i][k] / h;
+        for (j = l; j < m; j++) {
+          for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k];
+          for (k = l; k < n; k++) u[j][k] += s * rv1[k];
+        }
+        for (k = l; k < n; k++) u[i][k] *= scale;
+      }
+    }
+    anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i])));
+  }
+
+  for (i = n - 1; i >= 0; i--) {
+    if (i < n - 1) {
+      if (g != 0.) {
+        for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g;
+        for (j = l; j < n; j++) {
+          for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j];
+          for (k = l; k < n; k++) v[k][j] += s * v[k][i];
+        }
+      }
+      for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;
+    }
+    v[i][i] = 1.0;
+    g = rv1[i];
+    l = i;
+  }
+  for (i = AOMMIN(m, n) - 1; i >= 0; i--) {
+    l = i + 1;
+    g = w[i];
+    for (j = l; j < n; j++) u[i][j] = 0.0;
+    if (g != 0.) {
+      g = 1.0 / g;
+      for (j = l; j < n; j++) {
+        for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j];
+        f = (s / u[i][i]) * g;
+        for (k = i; k < m; k++) u[k][j] += f * u[k][i];
+      }
+      for (j = i; j < m; j++) u[j][i] *= g;
+    } else {
+      for (j = i; j < m; j++) u[j][i] = 0.0;
+    }
+    ++u[i][i];
+  }
+  for (k = n - 1; k >= 0; k--) {
+    for (its = 0; its < max_its; its++) {
+      flag = 1;
+      for (l = k; l >= 0; l--) {
+        nm = l - 1;
+        if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) {
+          flag = 0;
+          break;
+        }
+        if ((double)(fabs(w[nm]) + anorm) == anorm) break;
+      }
+      if (flag) {
+        c = 0.0;
+        s = 1.0;
+        for (i = l; i <= k; i++) {
+          f = s * rv1[i];
+          rv1[i] = c * rv1[i];
+          if ((double)(fabs(f) + anorm) == anorm) break;
+          g = w[i];
+          h = pythag(f, g);
+          w[i] = h;
+          h = 1.0 / h;
+          c = g * h;
+          s = -f * h;
+          for (j = 0; j < m; j++) {
+            y = u[j][nm];
+            z = u[j][i];
+            u[j][nm] = y * c + z * s;
+            u[j][i] = z * c - y * s;
+          }
+        }
+      }
+      z = w[k];
+      if (l == k) {
+        if (z < 0.0) {
+          w[k] = -z;
+          for (j = 0; j < n; j++) v[j][k] = -v[j][k];
+        }
+        break;
+      }
+      if (its == max_its - 1) {
+        aom_free(rv1);
+        return 1;
+      }
+      assert(k > 0);
+      x = w[l];
+      nm = k - 1;
+      y = w[nm];
+      g = rv1[nm];
+      h = rv1[k];
+      f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
+      g = pythag(f, 1.0);
+      f = ((x - z) * (x + z) + h * ((y / (f + sign(g, f))) - h)) / x;
+      c = s = 1.0;
+      for (j = l; j <= nm; j++) {
+        i = j + 1;
+        g = rv1[i];
+        y = w[i];
+        h = s * g;
+        g = c * g;
+        z = pythag(f, h);
+        rv1[j] = z;
+        c = f / z;
+        s = h / z;
+        f = x * c + g * s;
+        g = g * c - x * s;
+        h = y * s;
+        y *= c;
+        for (jj = 0; jj < n; jj++) {
+          x = v[jj][j];
+          z = v[jj][i];
+          v[jj][j] = x * c + z * s;
+          v[jj][i] = z * c - x * s;
+        }
+        z = pythag(f, h);
+        w[j] = z;
+        if (z != 0.) {
+          z = 1.0 / z;
+          c = f * z;
+          s = h * z;
+        }
+        f = c * g + s * y;
+        x = c * y - s * g;
+        for (jj = 0; jj < m; jj++) {
+          y = u[jj][j];
+          z = u[jj][i];
+          u[jj][j] = y * c + z * s;
+          u[jj][i] = z * c - y * s;
+        }
+      }
+      rv1[l] = 0.0;
+      rv1[k] = f;
+      w[k] = x;
+    }
+  }
+  aom_free(rv1);
+  return 0;
+}
+
+static int SVD(double *U, double *W, double *V, double *matx, int M, int N) {
+  // Assumes allocation for U is MxN
+  double **nrU = (double **)aom_malloc((M) * sizeof(*nrU));
+  double **nrV = (double **)aom_malloc((N) * sizeof(*nrV));
+  int problem, i;
+
+  problem = !(nrU && nrV);
+  if (!problem) {
+    for (i = 0; i < M; i++) {
+      nrU[i] = &U[i * N];
+    }
+    for (i = 0; i < N; i++) {
+      nrV[i] = &V[i * N];
+    }
+  } else {
+    if (nrU) aom_free(nrU);
+    if (nrV) aom_free(nrV);
+    return 1;
+  }
+
+  /* copy from given matx into nrU */
+  for (i = 0; i < M; i++) {
+    memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx));
+  }
+
+  /* HERE IT IS: do SVD */
+  if (svdcmp(nrU, M, N, W, nrV)) {
+    aom_free(nrU);
+    aom_free(nrV);
+    return 1;
+  }
+
+  /* aom_free Numerical Recipes arrays */
+  aom_free(nrU);
+  aom_free(nrV);
+
+  return 0;
+}
+
+int pseudo_inverse(double *inv, double *matx, const int M, const int N) {
+  double ans;
+  int i, j, k;
+  double *const U = (double *)aom_malloc(M * N * sizeof(*matx));
+  double *const W = (double *)aom_malloc(N * sizeof(*matx));
+  double *const V = (double *)aom_malloc(N * N * sizeof(*matx));
+
+  if (!(U && W && V)) {
+    return 1;
+  }
+  if (SVD(U, W, V, matx, M, N)) {
+    aom_free(U);
+    aom_free(W);
+    aom_free(V);
+    return 1;
+  }
+  for (i = 0; i < N; i++) {
+    if (fabs(W[i]) < TINY_NEAR_ZERO) {
+      aom_free(U);
+      aom_free(W);
+      aom_free(V);
+      return 1;
+    }
+  }
+
+  for (i = 0; i < N; i++) {
+    for (j = 0; j < M; j++) {
+      ans = 0;
+      for (k = 0; k < N; k++) {
+        ans += V[k + N * i] * U[k + N * j] / W[k];
+      }
+      inv[j + M * i] = ans;
+    }
+  }
+  aom_free(U);
+  aom_free(W);
+  aom_free(V);
+  return 0;
+}
+
+static void normalize_homography(double *pts, int n, double *T) {
+  double *p = pts;
+  double mean[2] = { 0, 0 };
+  double msqe = 0;
+  double scale;
+  int i;
+  for (i = 0; i < n; ++i, p += 2) {
+    mean[0] += p[0];
+    mean[1] += p[1];
+  }
+  mean[0] /= n;
+  mean[1] /= n;
+  for (p = pts, i = 0; i < n; ++i, p += 2) {
+    p[0] -= mean[0];
+    p[1] -= mean[1];
+    msqe += sqrt(p[0] * p[0] + p[1] * p[1]);
+  }
+  msqe /= n;
+  scale = (msqe == 0 ? 1.0 : sqrt(2) / msqe);
+  T[0] = scale;
+  T[1] = 0;
+  T[2] = -scale * mean[0];
+  T[3] = 0;
+  T[4] = scale;
+  T[5] = -scale * mean[1];
+  T[6] = 0;
+  T[7] = 0;
+  T[8] = 1;
+  for (p = pts, i = 0; i < n; ++i, p += 2) {
+    p[0] *= scale;
+    p[1] *= scale;
+  }
+}
+
+static void invnormalize_mat(double *T, double *iT) {
+  double is = 1.0 / T[0];
+  double m0 = -T[2] * is;
+  double m1 = -T[5] * is;
+  iT[0] = is;
+  iT[1] = 0;
+  iT[2] = m0;
+  iT[3] = 0;
+  iT[4] = is;
+  iT[5] = m1;
+  iT[6] = 0;
+  iT[7] = 0;
+  iT[8] = 1;
+}
+
+static void denormalize_homography(double *params, double *T1, double *T2) {
+  double iT2[9];
+  double params2[9];
+  invnormalize_mat(T2, iT2);
+  multiply_mat(params, T1, params2, 3, 3, 3);
+  multiply_mat(iT2, params2, params, 3, 3, 3);
+}
+
+static void denormalize_homography_reorder(double *params, double *T1,
+                                           double *T2) {
+  double params_denorm[MAX_PARAMDIM];
+  memcpy(params_denorm, params, sizeof(*params) * 8);
+  params_denorm[8] = 1.0;
+  denormalize_homography(params_denorm, T1, T2);
+  params[0] = params_denorm[2];
+  params[1] = params_denorm[5];
+  params[2] = params_denorm[0];
+  params[3] = params_denorm[1];
+  params[4] = params_denorm[3];
+  params[5] = params_denorm[4];
+  params[6] = params_denorm[6];
+  params[7] = params_denorm[7];
+}
+
+static void denormalize_affine_reorder(double *params, double *T1, double *T2) {
+  double params_denorm[MAX_PARAMDIM];
+  params_denorm[0] = params[0];
+  params_denorm[1] = params[1];
+  params_denorm[2] = params[4];
+  params_denorm[3] = params[2];
+  params_denorm[4] = params[3];
+  params_denorm[5] = params[5];
+  params_denorm[6] = params_denorm[7] = 0;
+  params_denorm[8] = 1;
+  denormalize_homography(params_denorm, T1, T2);
+  params[0] = params_denorm[2];
+  params[1] = params_denorm[5];
+  params[2] = params_denorm[0];
+  params[3] = params_denorm[1];
+  params[4] = params_denorm[3];
+  params[5] = params_denorm[4];
+  params[6] = params[7] = 0;
+}
+
+static void denormalize_rotzoom_reorder(double *params, double *T1,
+                                        double *T2) {
+  double params_denorm[MAX_PARAMDIM];
+  params_denorm[0] = params[0];
+  params_denorm[1] = params[1];
+  params_denorm[2] = params[2];
+  params_denorm[3] = -params[1];
+  params_denorm[4] = params[0];
+  params_denorm[5] = params[3];
+  params_denorm[6] = params_denorm[7] = 0;
+  params_denorm[8] = 1;
+  denormalize_homography(params_denorm, T1, T2);
+  params[0] = params_denorm[2];
+  params[1] = params_denorm[5];
+  params[2] = params_denorm[0];
+  params[3] = params_denorm[1];
+  params[4] = -params[3];
+  params[5] = params[2];
+  params[6] = params[7] = 0;
+}
+
+static void denormalize_translation_reorder(double *params, double *T1,
+                                            double *T2) {
+  double params_denorm[MAX_PARAMDIM];
+  params_denorm[0] = 1;
+  params_denorm[1] = 0;
+  params_denorm[2] = params[0];
+  params_denorm[3] = 0;
+  params_denorm[4] = 1;
+  params_denorm[5] = params[1];
+  params_denorm[6] = params_denorm[7] = 0;
+  params_denorm[8] = 1;
+  denormalize_homography(params_denorm, T1, T2);
+  params[0] = params_denorm[2];
+  params[1] = params_denorm[5];
+  params[2] = params[5] = 1;
+  params[3] = params[4] = 0;
+  params[6] = params[7] = 0;
+}
+
+static int find_translation(int np, double *pts1, double *pts2, double *mat) {
+  int i;
+  double sx, sy, dx, dy;
+  double sumx, sumy;
+
+  double T1[9], T2[9];
+  normalize_homography(pts1, np, T1);
+  normalize_homography(pts2, np, T2);
+
+  sumx = 0;
+  sumy = 0;
+  for (i = 0; i < np; ++i) {
+    dx = *(pts2++);
+    dy = *(pts2++);
+    sx = *(pts1++);
+    sy = *(pts1++);
+
+    sumx += dx - sx;
+    sumy += dy - sy;
+  }
+  mat[0] = sumx / np;
+  mat[1] = sumy / np;
+  denormalize_translation_reorder(mat, T1, T2);
+  return 0;
+}
+
+static int find_rotzoom(int np, double *pts1, double *pts2, double *mat) {
+  const int np2 = np * 2;
+  double *a = (double *)aom_malloc(sizeof(*a) * np2 * 9);
+  double *b = a + np2 * 4;
+  double *temp = b + np2;
+  int i;
+  double sx, sy, dx, dy;
+
+  double T1[9], T2[9];
+  normalize_homography(pts1, np, T1);
+  normalize_homography(pts2, np, T2);
+
+  for (i = 0; i < np; ++i) {
+    dx = *(pts2++);
+    dy = *(pts2++);
+    sx = *(pts1++);
+    sy = *(pts1++);
+
+    a[i * 2 * 4 + 0] = sx;
+    a[i * 2 * 4 + 1] = sy;
+    a[i * 2 * 4 + 2] = 1;
+    a[i * 2 * 4 + 3] = 0;
+    a[(i * 2 + 1) * 4 + 0] = sy;
+    a[(i * 2 + 1) * 4 + 1] = -sx;
+    a[(i * 2 + 1) * 4 + 2] = 0;
+    a[(i * 2 + 1) * 4 + 3] = 1;
+
+    b[2 * i] = dx;
+    b[2 * i + 1] = dy;
+  }
+  if (pseudo_inverse(temp, a, np2, 4)) {
+    aom_free(a);
+    return 1;
+  }
+  multiply_mat(temp, b, mat, 4, np2, 1);
+  denormalize_rotzoom_reorder(mat, T1, T2);
+  aom_free(a);
+  return 0;
+}
+
+static int find_affine(int np, double *pts1, double *pts2, double *mat) {
+  const int np2 = np * 2;
+  double *a = (double *)aom_malloc(sizeof(*a) * np2 * 13);
+  double *b = a + np2 * 6;
+  double *temp = b + np2;
+  int i;
+  double sx, sy, dx, dy;
+
+  double T1[9], T2[9];
+  normalize_homography(pts1, np, T1);
+  normalize_homography(pts2, np, T2);
+
+  for (i = 0; i < np; ++i) {
+    dx = *(pts2++);
+    dy = *(pts2++);
+    sx = *(pts1++);
+    sy = *(pts1++);
+
+    a[i * 2 * 6 + 0] = sx;
+    a[i * 2 * 6 + 1] = sy;
+    a[i * 2 * 6 + 2] = 0;
+    a[i * 2 * 6 + 3] = 0;
+    a[i * 2 * 6 + 4] = 1;
+    a[i * 2 * 6 + 5] = 0;
+    a[(i * 2 + 1) * 6 + 0] = 0;
+    a[(i * 2 + 1) * 6 + 1] = 0;
+    a[(i * 2 + 1) * 6 + 2] = sx;
+    a[(i * 2 + 1) * 6 + 3] = sy;
+    a[(i * 2 + 1) * 6 + 4] = 0;
+    a[(i * 2 + 1) * 6 + 5] = 1;
+
+    b[2 * i] = dx;
+    b[2 * i + 1] = dy;
+  }
+  if (pseudo_inverse(temp, a, np2, 6)) {
+    aom_free(a);
+    return 1;
+  }
+  multiply_mat(temp, b, mat, 6, np2, 1);
+  denormalize_affine_reorder(mat, T1, T2);
+  aom_free(a);
+  return 0;
+}
+
+static int find_vertrapezoid(int np, double *pts1, double *pts2, double *mat) {
+  const int np3 = np * 3;
+  double *a = (double *)aom_malloc(sizeof(*a) * np3 * 14);
+  double *U = a + np3 * 7;
+  double S[7], V[7 * 7], H[9];
+  int i, mini;
+  double sx, sy, dx, dy;
+  double T1[9], T2[9];
+
+  normalize_homography(pts1, np, T1);
+  normalize_homography(pts2, np, T2);
+
+  for (i = 0; i < np; ++i) {
+    dx = *(pts2++);
+    dy = *(pts2++);
+    sx = *(pts1++);
+    sy = *(pts1++);
+
+    a[i * 3 * 7 + 0] = a[i * 3 * 7 + 1] = 0;
+    a[i * 3 * 7 + 2] = -sx;
+    a[i * 3 * 7 + 3] = -sy;
+    a[i * 3 * 7 + 4] = -1;
+    a[i * 3 * 7 + 5] = dy * sx;
+    a[i * 3 * 7 + 6] = dy;
+
+    a[(i * 3 + 1) * 7 + 0] = sx;
+    a[(i * 3 + 1) * 7 + 1] = 1;
+    a[(i * 3 + 1) * 7 + 2] = a[(i * 3 + 1) * 7 + 3] = a[(i * 3 + 1) * 7 + 4] =
+        0;
+    a[(i * 3 + 1) * 7 + 5] = -dx * sx;
+    a[(i * 3 + 1) * 7 + 6] = -dx;
+
+    a[(i * 3 + 2) * 7 + 0] = -dy * sx;
+    a[(i * 3 + 2) * 7 + 1] = -dy;
+    a[(i * 3 + 2) * 7 + 2] = dx * sx;
+    a[(i * 3 + 2) * 7 + 3] = dx * sy;
+    a[(i * 3 + 2) * 7 + 4] = dx;
+    a[(i * 3 + 2) * 7 + 5] = a[(i * 3 + 2) * 7 + 6] = 0;
+  }
+  if (SVD(U, S, V, a, np3, 7)) {
+    aom_free(a);
+    return 1;
+  } else {
+    double minS = 1e12;
+    mini = -1;
+    for (i = 0; i < 7; ++i) {
+      if (S[i] < minS) {
+        minS = S[i];
+        mini = i;
+      }
+    }
+  }
+  H[1] = H[7] = 0;
+  for (i = 0; i < 1; i++) H[i] = V[i * 7 + mini];
+  for (; i < 6; i++) H[i + 1] = V[i * 7 + mini];
+  for (; i < 7; i++) H[i + 2] = V[i * 7 + mini];
+
+  denormalize_homography_reorder(H, T1, T2);
+  aom_free(a);
+  if (H[8] == 0.0) {
+    return 1;
+  } else {
+    // normalize
+    double f = 1.0 / H[8];
+    for (i = 0; i < 8; i++) mat[i] = f * H[i];
+  }
+  return 0;
+}
+
+static int find_hortrapezoid(int np, double *pts1, double *pts2, double *mat) {
+  const int np3 = np * 3;
+  double *a = (double *)aom_malloc(sizeof(*a) * np3 * 14);
+  double *U = a + np3 * 7;
+  double S[7], V[7 * 7], H[9];
+  int i, mini;
+  double sx, sy, dx, dy;
+  double T1[9], T2[9];
+
+  normalize_homography(pts1, np, T1);
+  normalize_homography(pts2, np, T2);
+
+  for (i = 0; i < np; ++i) {
+    dx = *(pts2++);
+    dy = *(pts2++);
+    sx = *(pts1++);
+    sy = *(pts1++);
+
+    a[i * 3 * 7 + 0] = a[i * 3 * 7 + 1] = a[i * 3 * 7 + 2] = 0;
+    a[i * 3 * 7 + 3] = -sy;
+    a[i * 3 * 7 + 4] = -1;
+    a[i * 3 * 7 + 5] = dy * sy;
+    a[i * 3 * 7 + 6] = dy;
+
+    a[(i * 3 + 1) * 7 + 0] = sx;
+    a[(i * 3 + 1) * 7 + 1] = sy;
+    a[(i * 3 + 1) * 7 + 2] = 1;
+    a[(i * 3 + 1) * 7 + 3] = a[(i * 3 + 1) * 7 + 4] = 0;
+    a[(i * 3 + 1) * 7 + 5] = -dx * sy;
+    a[(i * 3 + 1) * 7 + 6] = -dx;
+
+    a[(i * 3 + 2) * 7 + 0] = -dy * sx;
+    a[(i * 3 + 2) * 7 + 1] = -dy * sy;
+    a[(i * 3 + 2) * 7 + 2] = -dy;
+    a[(i * 3 + 2) * 7 + 3] = dx * sy;
+    a[(i * 3 + 2) * 7 + 4] = dx;
+    a[(i * 3 + 2) * 7 + 5] = a[(i * 3 + 2) * 7 + 6] = 0;
+  }
+
+  if (SVD(U, S, V, a, np3, 7)) {
+    aom_free(a);
+    return 1;
+  } else {
+    double minS = 1e12;
+    mini = -1;
+    for (i = 0; i < 7; ++i) {
+      if (S[i] < minS) {
+        minS = S[i];
+        mini = i;
+      }
+    }
+  }
+  H[3] = H[6] = 0;
+  for (i = 0; i < 3; i++) H[i] = V[i * 7 + mini];
+  for (; i < 5; i++) H[i + 1] = V[i * 7 + mini];
+  for (; i < 7; i++) H[i + 2] = V[i * 7 + mini];
+
+  denormalize_homography_reorder(H, T1, T2);
+  aom_free(a);
+  if (H[8] == 0.0) {
+    return 1;
+  } else {
+    // normalize
+    double f = 1.0 / H[8];
+    for (i = 0; i < 8; i++) mat[i] = f * H[i];
+  }
+  return 0;
+}
+
+static int find_homography(int np, double *pts1, double *pts2, double *mat) {
+  // Implemented from Peter Kovesi's normalized implementation
+  const int np3 = np * 3;
+  double *a = (double *)aom_malloc(sizeof(*a) * np3 * 18);
+  double *U = a + np3 * 9;
+  double S[9], V[9 * 9], H[9];
+  int i, mini;
+  double sx, sy, dx, dy;
+  double T1[9], T2[9];
+
+  normalize_homography(pts1, np, T1);
+  normalize_homography(pts2, np, T2);
+
+  for (i = 0; i < np; ++i) {
+    dx = *(pts2++);
+    dy = *(pts2++);
+    sx = *(pts1++);
+    sy = *(pts1++);
+
+    a[i * 3 * 9 + 0] = a[i * 3 * 9 + 1] = a[i * 3 * 9 + 2] = 0;
+    a[i * 3 * 9 + 3] = -sx;
+    a[i * 3 * 9 + 4] = -sy;
+    a[i * 3 * 9 + 5] = -1;
+    a[i * 3 * 9 + 6] = dy * sx;
+    a[i * 3 * 9 + 7] = dy * sy;
+    a[i * 3 * 9 + 8] = dy;
+
+    a[(i * 3 + 1) * 9 + 0] = sx;
+    a[(i * 3 + 1) * 9 + 1] = sy;
+    a[(i * 3 + 1) * 9 + 2] = 1;
+    a[(i * 3 + 1) * 9 + 3] = a[(i * 3 + 1) * 9 + 4] = a[(i * 3 + 1) * 9 + 5] =
+        0;
+    a[(i * 3 + 1) * 9 + 6] = -dx * sx;
+    a[(i * 3 + 1) * 9 + 7] = -dx * sy;
+    a[(i * 3 + 1) * 9 + 8] = -dx;
+
+    a[(i * 3 + 2) * 9 + 0] = -dy * sx;
+    a[(i * 3 + 2) * 9 + 1] = -dy * sy;
+    a[(i * 3 + 2) * 9 + 2] = -dy;
+    a[(i * 3 + 2) * 9 + 3] = dx * sx;
+    a[(i * 3 + 2) * 9 + 4] = dx * sy;
+    a[(i * 3 + 2) * 9 + 5] = dx;
+    a[(i * 3 + 2) * 9 + 6] = a[(i * 3 + 2) * 9 + 7] = a[(i * 3 + 2) * 9 + 8] =
+        0;
+  }
+
+  if (SVD(U, S, V, a, np3, 9)) {
+    aom_free(a);
+    return 1;
+  } else {
+    double minS = 1e12;
+    mini = -1;
+    for (i = 0; i < 9; ++i) {
+      if (S[i] < minS) {
+        minS = S[i];
+        mini = i;
+      }
+    }
+  }
+
+  for (i = 0; i < 9; i++) H[i] = V[i * 9 + mini];
+  denormalize_homography_reorder(H, T1, T2);
+  aom_free(a);
+  if (H[8] == 0.0) {
+    return 1;
+  } else {
+    // normalize
+    double f = 1.0 / H[8];
+    for (i = 0; i < 8; i++) mat[i] = f * H[i];
+  }
+  return 0;
+}
+
+static int get_rand_indices(int npoints, int minpts, int *indices,
+                            unsigned int *seed) {
+  int i, j;
+  int ptr = rand_r(seed) % npoints;
+  if (minpts > npoints) return 0;
+  indices[0] = ptr;
+  ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
+  i = 1;
+  while (i < minpts) {
+    int index = rand_r(seed) % npoints;
+    while (index) {
+      ptr = (ptr == npoints - 1 ? 0 : ptr + 1);
+      for (j = 0; j < i; ++j) {
+        if (indices[j] == ptr) break;
+      }
+      if (j == i) index--;
+    }
+    indices[i++] = ptr;
+  }
+  return 1;
+}
+
+typedef struct {
+  int num_inliers;
+  double variance;
+  int *inlier_indices;
+} RANSAC_MOTION;
+
+// Return -1 if 'a' is a better motion, 1 if 'b' is better, 0 otherwise.
+static int compare_motions(const void *arg_a, const void *arg_b) {
+  const RANSAC_MOTION *motion_a = (RANSAC_MOTION *)arg_a;
+  const RANSAC_MOTION *motion_b = (RANSAC_MOTION *)arg_b;
+
+  if (motion_a->num_inliers > motion_b->num_inliers) return -1;
+  if (motion_a->num_inliers < motion_b->num_inliers) return 1;
+  if (motion_a->variance < motion_b->variance) return -1;
+  if (motion_a->variance > motion_b->variance) return 1;
+  return 0;
+}
+
+static int is_better_motion(const RANSAC_MOTION *motion_a,
+                            const RANSAC_MOTION *motion_b) {
+  return compare_motions(motion_a, motion_b) < 0;
+}
+
+static void copy_points_at_indices(double *dest, const double *src,
+                                   const int *indices, int num_points) {
+  for (int i = 0; i < num_points; ++i) {
+    const int index = indices[i];
+    dest[i * 2] = src[index * 2];
+    dest[i * 2 + 1] = src[index * 2 + 1];
+  }
+}
+
+static const double kInfiniteVariance = 1e12;
+
+static void clear_motion(RANSAC_MOTION *motion, int num_points) {
+  motion->num_inliers = 0;
+  motion->variance = kInfiniteVariance;
+  memset(motion->inlier_indices, 0,
+         sizeof(*motion->inlier_indices * num_points));
+}
+
+static int ransac(const int *matched_points, int npoints,
+                  int *num_inliers_by_motion, double *params_by_motion,
+                  int num_desired_motions, const int minpts,
+                  IsDegenerateFunc is_degenerate,
+                  FindTransformationFunc find_transformation,
+                  ProjectPointsDoubleFunc projectpoints) {
+  static const double PROBABILITY_REQUIRED = 0.9;
+  static const double EPS = 1e-12;
+
+  int N = 10000, trial_count = 0;
+  int i = 0;
+  int ret_val = 0;
+
+  unsigned int seed = (unsigned int)npoints;
+
+  int indices[MAX_MINPTS] = { 0 };
+
+  double *points1, *points2;
+  double *corners1, *corners2;
+  double *image1_coord;
+
+  // Store information for the num_desired_motions best transformations found
+  // and the worst motion among them, as well as the motion currently under
+  // consideration.
+  RANSAC_MOTION *motions, *worst_kept_motion = NULL;
+  RANSAC_MOTION current_motion;
+
+  // Store the parameters and the indices of the inlier points for the motion
+  // currently under consideration.
+  double params_this_motion[MAX_PARAMDIM];
+
+  double *cnp1, *cnp2;
+
+  if (npoints < minpts * MINPTS_MULTIPLIER || npoints == 0) {
+    return 1;
+  }
+
+  points1 = (double *)aom_malloc(sizeof(*points1) * npoints * 2);
+  points2 = (double *)aom_malloc(sizeof(*points2) * npoints * 2);
+  corners1 = (double *)aom_malloc(sizeof(*corners1) * npoints * 2);
+  corners2 = (double *)aom_malloc(sizeof(*corners2) * npoints * 2);
+  image1_coord = (double *)aom_malloc(sizeof(*image1_coord) * npoints * 2);
+
+  motions =
+      (RANSAC_MOTION *)aom_malloc(sizeof(RANSAC_MOTION) * num_desired_motions);
+  for (i = 0; i < num_desired_motions; ++i) {
+    motions[i].inlier_indices =
+        (int *)aom_malloc(sizeof(*motions->inlier_indices) * npoints);
+    clear_motion(motions + i, npoints);
+  }
+  current_motion.inlier_indices =
+      (int *)aom_malloc(sizeof(*current_motion.inlier_indices) * npoints);
+  clear_motion(&current_motion, npoints);
+
+  worst_kept_motion = motions;
+
+  if (!(points1 && points2 && corners1 && corners2 && image1_coord && motions &&
+        current_motion.inlier_indices)) {
+    ret_val = 1;
+    goto finish_ransac;
+  }
+
+  cnp1 = corners1;
+  cnp2 = corners2;
+  for (i = 0; i < npoints; ++i) {
+    *(cnp1++) = *(matched_points++);
+    *(cnp1++) = *(matched_points++);
+    *(cnp2++) = *(matched_points++);
+    *(cnp2++) = *(matched_points++);
+  }
+
+  while (N > trial_count) {
+    double sum_distance = 0.0;
+    double sum_distance_squared = 0.0;
+
+    clear_motion(&current_motion, npoints);
+
+    int degenerate = 1;
+    int num_degenerate_iter = 0;
+
+    while (degenerate) {
+      num_degenerate_iter++;
+      if (!get_rand_indices(npoints, minpts, indices, &seed)) {
+        ret_val = 1;
+        goto finish_ransac;
+      }
+
+      copy_points_at_indices(points1, corners1, indices, minpts);
+      copy_points_at_indices(points2, corners2, indices, minpts);
+
+      degenerate = is_degenerate(points1);
+      if (num_degenerate_iter > MAX_DEGENERATE_ITER) {
+        ret_val = 1;
+        goto finish_ransac;
+      }
+    }
+
+    if (find_transformation(minpts, points1, points2, params_this_motion)) {
+      trial_count++;
+      continue;
+    }
+
+    projectpoints(params_this_motion, corners1, image1_coord, npoints, 2, 2);
+
+    for (i = 0; i < npoints; ++i) {
+      double dx = image1_coord[i * 2] - corners2[i * 2];
+      double dy = image1_coord[i * 2 + 1] - corners2[i * 2 + 1];
+      double distance = sqrt(dx * dx + dy * dy);
+
+      if (distance < INLIER_THRESHOLD) {
+        current_motion.inlier_indices[current_motion.num_inliers++] = i;
+        sum_distance += distance;
+        sum_distance_squared += distance * distance;
+      }
+    }
+
+    if (current_motion.num_inliers >= worst_kept_motion->num_inliers &&
+        current_motion.num_inliers > 1) {
+      int temp;
+      double fracinliers, pNoOutliers, mean_distance;
+      mean_distance = sum_distance / ((double)current_motion.num_inliers);
+      current_motion.variance =
+          sum_distance_squared / ((double)current_motion.num_inliers - 1.0) -
+          mean_distance * mean_distance * ((double)current_motion.num_inliers) /
+              ((double)current_motion.num_inliers - 1.0);
+      if (is_better_motion(&current_motion, worst_kept_motion)) {
+        // This motion is better than the worst currently kept motion. Remember
+        // the inlier points and variance. The parameters for each kept motion
+        // will be recomputed later using only the inliers.
+        worst_kept_motion->num_inliers = current_motion.num_inliers;
+        worst_kept_motion->variance = current_motion.variance;
+        memcpy(worst_kept_motion->inlier_indices, current_motion.inlier_indices,
+               sizeof(*current_motion.inlier_indices) * npoints);
+
+        assert(npoints > 0);
+        fracinliers = (double)current_motion.num_inliers / (double)npoints;
+        pNoOutliers = 1 - pow(fracinliers, minpts);
+        pNoOutliers = fmax(EPS, pNoOutliers);
+        pNoOutliers = fmin(1 - EPS, pNoOutliers);
+        temp = (int)(log(1.0 - PROBABILITY_REQUIRED) / log(pNoOutliers));
+
+        if (temp > 0 && temp < N) {
+          N = AOMMAX(temp, MIN_TRIALS);
+        }
+
+        // Determine the new worst kept motion and its num_inliers and variance.
+        for (i = 0; i < num_desired_motions; ++i) {
+          if (is_better_motion(worst_kept_motion, &motions[i])) {
+            worst_kept_motion = &motions[i];
+          }
+        }
+      }
+    }
+    trial_count++;
+  }
+
+  // Sort the motions, best first.
+  qsort(motions, num_desired_motions, sizeof(RANSAC_MOTION), compare_motions);
+
+  // Recompute the motions using only the inliers.
+  for (i = 0; i < num_desired_motions; ++i) {
+    copy_points_at_indices(points1, corners1, motions[i].inlier_indices,
+                           motions[i].num_inliers);
+    copy_points_at_indices(points2, corners2, motions[i].inlier_indices,
+                           motions[i].num_inliers);
+
+    find_transformation(motions[i].num_inliers, points1, points2,
+                        params_by_motion + (MAX_PARAMDIM - 1) * i);
+    num_inliers_by_motion[i] = motions[i].num_inliers;
+  }
+
+finish_ransac:
+  aom_free(points1);
+  aom_free(points2);
+  aom_free(corners1);
+  aom_free(corners2);
+  aom_free(image1_coord);
+  aom_free(current_motion.inlier_indices);
+  for (i = 0; i < num_desired_motions; ++i) {
+    aom_free(motions[i].inlier_indices);
+  }
+  aom_free(motions);
+
+  return ret_val;
+}
+
+static int is_collinear3(double *p1, double *p2, double *p3) {
+  static const double collinear_eps = 1e-3;
+  const double v =
+      (p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0]);
+  return fabs(v) < collinear_eps;
+}
+
+static int is_degenerate_translation(double *p) {
+  return (p[0] - p[2]) * (p[0] - p[2]) + (p[1] - p[3]) * (p[1] - p[3]) <= 2;
+}
+
+static int is_degenerate_affine(double *p) {
+  return is_collinear3(p, p + 2, p + 4);
+}
+
+static int is_degenerate_homography(double *p) {
+  return is_collinear3(p, p + 2, p + 4) || is_collinear3(p, p + 2, p + 6) ||
+         is_collinear3(p, p + 4, p + 6) || is_collinear3(p + 2, p + 4, p + 6);
+}
+
+int ransac_translation(int *matched_points, int npoints,
+                       int *num_inliers_by_motion, double *params_by_motion,
+                       int num_desired_motions) {
+  return ransac(matched_points, npoints, num_inliers_by_motion,
+                params_by_motion, num_desired_motions, 3,
+                is_degenerate_translation, find_translation,
+                project_points_double_translation);
+}
+
+int ransac_rotzoom(int *matched_points, int npoints, int *num_inliers_by_motion,
+                   double *params_by_motion, int num_desired_motions) {
+  return ransac(matched_points, npoints, num_inliers_by_motion,
+                params_by_motion, num_desired_motions, 3, is_degenerate_affine,
+                find_rotzoom, project_points_double_rotzoom);
+}
+
+int ransac_affine(int *matched_points, int npoints, int *num_inliers_by_motion,
+                  double *params_by_motion, int num_desired_motions) {
+  return ransac(matched_points, npoints, num_inliers_by_motion,
+                params_by_motion, num_desired_motions, 3, is_degenerate_affine,
+                find_affine, project_points_double_affine);
+}
+
+int ransac_homography(int *matched_points, int npoints,
+                      int *num_inliers_by_motion, double *params_by_motion,
+                      int num_desired_motions) {
+  return ransac(matched_points, npoints, num_inliers_by_motion,
+                params_by_motion, num_desired_motions, 4,
+                is_degenerate_homography, find_homography,
+                project_points_double_homography);
+}
+
+int ransac_hortrapezoid(int *matched_points, int npoints,
+                        int *num_inliers_by_motion, double *params_by_motion,
+                        int num_desired_motions) {
+  return ransac(matched_points, npoints, num_inliers_by_motion,
+                params_by_motion, num_desired_motions, 4,
+                is_degenerate_homography, find_hortrapezoid,
+                project_points_double_hortrapezoid);
+}
+
+int ransac_vertrapezoid(int *matched_points, int npoints,
+                        int *num_inliers_by_motion, double *params_by_motion,
+                        int num_desired_motions) {
+  return ransac(matched_points, npoints, num_inliers_by_motion,
+                params_by_motion, num_desired_motions, 4,
+                is_degenerate_homography, find_vertrapezoid,
+                project_points_double_vertrapezoid);
+}