static void so_sparse_matrix_add(so_sparse_entries_t matrix, int index, float value)
{
if (matrix.count == matrix.capacity)
{
int newCapacity = matrix.capacity * 2;
if (newCapacity < 64)
{
newCapacity = 64;
}
so_sparse_entry_t[] newEntries = new so_sparse_entry_t[newCapacity];
for (int i = 0; i < matrix.count; i++)
{
newEntries[i] = matrix.entries[i];
}
for (int i = matrix.count; i < newCapacity; i++)
{
newEntries[i] = new so_sparse_entry_t(-1, 0);
}
matrix.entries = newEntries;
matrix.capacity = newCapacity;
}
int entryIndex = matrix.count++;
matrix.entries[entryIndex].index = index;
matrix.entries[entryIndex].value = value;
}
static void so_matrix_cholesky_solve(so_sparse_entries_t Lrows, so_sparse_entries_t Lcols, float[] x, float[] b, int n)
{
float[] y = new float[n];
// L * y = b
int Lindex = 0;
for (int i = 0; i < n; i++)
{
float sum = b[i];
while (Lindex < Lrows.count && Lrows.entries[Lindex].index < i * (n + 1))
{
sum -= Lrows.entries[Lindex].value * y[Lrows.entries[Lindex].index - i * n];
++Lindex;
}
Debug.Assert(Lrows.entries[Lindex].index == i * (n + 1));
y[i] = sum / Lrows.entries[Lindex].value;
++Lindex;
}
// L' * x = y
Lindex = Lcols.count - 1;
for (int i = n - 1; i >= 0; i--)
{
float sum = y[i];
while (Lindex >= 0 && Lcols.entries[Lindex].index > i * (n + 1))
{
sum -= Lcols.entries[Lindex].value * x[Lcols.entries[Lindex].index - i * n];
--Lindex;
}
Debug.Assert(Lcols.entries[Lindex].index == i * (n + 1));
x[i] = sum / Lcols.entries[Lindex].value;
--Lindex;
}
}
static so_sparse_entry_t so_sparse_entry_set_get_or_add(so_sparse_entries_t set, int index)
{
if (set.count + 1 > set.capacity * 3 / 4) // leave some free space to avoid having many collisions
{
int newCapacity = set.capacity >= 64 ? set.capacity * 2 : 64;
so_sparse_entry_t[] newEntries = new so_sparse_entry_t[newCapacity];
for (int i = 0; i < newCapacity; i++)
{
newEntries[i] = new so_sparse_entry_t(-1, 0);
}
for (int i = 0; i < set.capacity; i++) // rehash all old entries
{
if (set.entries[i].index != -1)
{
int hash_ = so_sparse_entry_hash(set.entries[i].index, newCapacity);
while (newEntries[hash_].index != -1) // collisions
{
hash_ = (hash_ + 1) % newCapacity;
}
newEntries[hash_] = set.entries[i];
}
}
set.entries = newEntries;
set.capacity = newCapacity;
}
int hash = so_sparse_entry_hash(index, set.capacity);
while (set.entries[hash].index != -1) // collisions
{
if (set.entries[hash].index == index)
{
return(set.entries[hash]); // entry is already in the set
}
hash = (hash + 1) % set.capacity;
}
if (set.entries[hash].index == -1) // make new entry
{
set.entries[hash].index = index;
set.entries[hash].value = 0.0f;
set.count++;
return(set.entries[hash]);
}
Debug.Assert(false);
return(null); // shouldn't happen
}
static so_sparse_entries_t so_matrix_At_times_A(float[] A, int[] sparseIndices, int maxRowIndices, int m, int n)
{
so_sparse_entries_t AtA = new so_sparse_entries_t((n / 16) * (n / 16));
// compute lower left triangle only since the result is symmetric
for (int k = 0; k < m; k++)
{
int srcPtr = k * maxRowIndices;
int indexPtr = k * maxRowIndices;
for (int i = 0; i < maxRowIndices; i++)
{
int index_i = sparseIndices[indexPtr + i];
if (index_i < 0)
{
break;
}
float v = A[srcPtr + i];
//float *dstPtr = AtA + index_i * n;
for (int j = 0; j < maxRowIndices; j++)
{
int index_j = sparseIndices[indexPtr + j];
if (index_j < 0)
{
break;
}
//dstPtr[index_j] += v * srcPtr[j];
int index = index_i * n + index_j;
so_sparse_entry_t entry = so_sparse_entry_set_get_or_add(AtA, index);
entry.value += v * A[srcPtr + j];
}
}
}
// compaction step (make a compact array from the scattered hash set values)
for (int i = 0, j = 0; i < AtA.capacity; i++)
{
if (AtA.entries[i].index != -1)
{
AtA.entries[j++] = AtA.entries[i];
}
}
// sort by index . this is a sparse matrix now
so_sparse_matrix_sort(AtA);
return(AtA);
}
static bool so_sparse_matrix_advance_to_index(so_sparse_entries_t matrix, ref int position, int index, ref float outValue)
{
int localPosition = position;
while (localPosition < matrix.count && matrix.entries[localPosition].index < index)
{
++localPosition;
}
position = localPosition;
if (localPosition < matrix.count && matrix.entries[localPosition].index == index)
{
outValue = matrix.entries[localPosition].value;
return(true);
}
return(false);
}
public static bool so_seam_optimize(so_seam_t seam, Color[] data, int w, int h, int c = 3, float lambda = 0.1f)
{
so_texel_set_t texels = seam.texels;
so_stitching_points_t stitchingPoints = seam.stitchingPoints;
int m = stitchingPoints.count;
int n = texels.count;
so_texel_t[] texelsFlat = new so_texel_t[n];
for (int i = 0; i < n; i++)
{
texelsFlat[i] = new so_texel_t(0, 0);
}
float[] A = new float[(m + n) * 8];
int[] AsparseIndices = new int[(m + n) * 8];
float[] b = new float[m + n];
float[] Atb = new float[n];
float[] x = new float[n];
for (int i = 0, j = 0; i < texels.capacity && j < n; i++)
{
if (texels.texels[i].x != -1)
{
texelsFlat[j++] = texels.texels[i];
}
}
System.Array.Sort(texelsFlat, so_texel_cmp);
int r = 0;
for (int i = 0; i < m; i++)
{
int[] column0 = { 0, 0, 0, 0 };
int[] column1 = { 0, 0, 0, 0 };
bool side0valid = false, side1valid = false;
for (int k = 0; k < 4; k++)
{
so_texel_t t0 = stitchingPoints.points[i].sides[0].texels[k];
so_texel_t t1 = stitchingPoints.points[i].sides[1].texels[k];
column0[k] = System.Array.BinarySearch(texelsFlat, t0, so_texel_cmp);
column1[k] = System.Array.BinarySearch(texelsFlat, t1, so_texel_cmp);
if (column0[k] == -1)
{
side0valid = false; break;
}
if (column1[k] == -1)
{
side1valid = false; break;
}
// test for validity of stitching point
for (int ci = 0; ci < c; ci++)
{
side0valid |= data[t0.y * w + t0.x][ci] > 0.0f;
side1valid |= data[t1.y * w + t1.x][ci] > 0.0f;
}
}
if (side0valid && side1valid)
{
for (int k = 0; k < 4; k++)
{
A[r * 8 + k * 2 + 0] = stitchingPoints.points[i].sides[0].weights[k];
AsparseIndices[r * 8 + k * 2 + 0] = column0[k];
A[r * 8 + k * 2 + 1] = -stitchingPoints.points[i].sides[1].weights[k];
AsparseIndices[r * 8 + k * 2 + 1] = column1[k];
}
r++;
}
}
m = r;
// add error terms for deviation from original pixel value (scaled by lambda)
for (int i = 0; i < n; i++)
{
A[(m + i) * 8] = lambda;
AsparseIndices[(m + i) * 8 + 0] = i;
AsparseIndices[(m + i) * 8 + 1] = -1;
}
so_sparse_entries_t AtA = so_matrix_At_times_A(A, AsparseIndices, 8, m + n, n);
so_sparse_entries_t L = so_matrix_cholesky_prepare(AtA, n);
if (L.count == 0)
{
return(false); // Cholesky decomposition failed
}
so_sparse_entries_t Lcols = new so_sparse_entries_t(L.count);
for (int i = 0; i < L.count; i++)
{
so_sparse_matrix_add(Lcols, (L.entries[i].index % n) * n + (L.entries[i].index / n), L.entries[i].value);
}
so_sparse_matrix_sort(Lcols);
// solve each color channel independently
for (int ci = 0; ci < c; ci++)
{
for (int i = 0; i < n; i++)
{
b[m + i] = lambda * data[texelsFlat[i].y * w + texelsFlat[i].x][ci];
}
so_matrix_At_times_b(A, m + n, n, b, Atb, AsparseIndices, 8);
so_matrix_cholesky_solve(L, Lcols, x, Atb, n);
// write out results
for (int i = 0; i < n; i++)
{
data[texelsFlat[i].y * w + texelsFlat[i].x][ci] = Mathf.Max(x[i], 0);
}
}
return(true);
}
static so_sparse_entries_t so_matrix_cholesky_prepare(so_sparse_entries_t AtA, int n)
{
// dense
//for (int i = 0; i < n; i++)
//{
// float *a = L + i * n;
// for (int j = 0; j <= i; j++)
// {
// float *b = L + j * n;
// float sum = A[i * n + j];// + (i == j ? 0.0001 : 0.0); // some regularization
// for (int k = 0; k < j; k++)
// sum -= a[k] * b[k];
// if (i > j)
// a[j] = sum / b[j];
// else // i == j
// {
// if (sum <= 0.0)
// return false;
// a[i] = sqrtf(sum);
// }
// }
//}
// sparse
int[] indices_i = new int[n];
float[] row_i = new float[n];
float[] invDiag = new float[n];
so_sparse_entries_t L = new so_sparse_entries_t((n / 16) * (n / 16));
int AtAindex = 0;
for (int i = 0; i < n; i++)
{
int index_i_count = 0;
int row_j_index = 0;
for (int j = 0; j <= i; j++)
{
//float sum = A[i * n + j]; // + (i == j ? 0.0001 : 0.0); // regularization
int index = i * n + j;
float sum = 0.0f;
so_sparse_matrix_advance_to_index(AtA, ref AtAindex, index, ref sum);
for (int k = 0; k < index_i_count; k++)
{
int index_i = indices_i[k];
float Lvalue = 0;
if (so_sparse_matrix_advance_to_index(L, ref row_j_index, j * n + index_i, ref Lvalue))
{
sum -= row_i[index_i] * Lvalue;
}
}
if (i == j)
{
if (sum <= 0.0f)
{
return(L);
}
invDiag[i] = 1.0f / Mathf.Sqrt(sum);
}
if (Mathf.Abs(sum) > 0.00001f)
{
row_i[j] = sum * invDiag[j];
indices_i[index_i_count++] = j;
so_sparse_matrix_add(L, index, row_i[j]);
}
else
{
row_i[j] = 0.0f;
}
}
}
return(L);
}
static void so_sparse_matrix_sort(so_sparse_entries_t matrix)
{
System.Array.Sort(matrix.entries, 0, matrix.count, so_sparse_entry_cmp);
}
