def _calculate_r(rff, dx, dy, wx, wy, nrows, ncols):
# Center of the matrix - point with maximum value
center_line, center_column = np.unravel_index(rff.argmax(), rff.shape)
# Number of images
p = len(dx)
k = (p * wx * wy) / (nrows * ncols)
# Reference vectors
xv = np.arange(0, wx/nrows) + 1
yv = np.arange(0, wy/ncols) + 1
ref_line, ref_column = np.meshgrid(xv, yv)
ref_line = mt.vectorize_matrix(ref_line)
ref_column = mt.vectorize_matrix(ref_column)
# Initialize matrix
zeros = np.zeros(9)
ref_v_line = mt.generate_and_flatten_grid(zeros, ref_line, 'Y')
ref_v_column = mt.generate_and_flatten_grid(zeros, ref_column, 'Y')
# Inner loop - fill R's columns - line vectors
inner_ref_m_column = np.meshgrid(ref_v_column, ref_v_column)[0] * 3
inner_ref_m_line = np.meshgrid(ref_v_line, ref_v_line)[0] * 3
# Outer loop - fill R's lines - column vectors
outer_ref_m_line = inner_ref_m_line.T
outer_ref_m_column = inner_ref_m_column.T
# Include motion matrices
yv = np.arange(k/p) + 1
motion_line = mt.generate_and_flatten_grid(dy, yv, 'X')
motion_column = mt.generate_and_flatten_grid(dx, yv, 'X')
# Matrices with reference values of the motion vectors
# Each image block is a line vector with dx*dy width
tmp_v = np.arange(k) + 1
ref_motion_line = np.meshgrid(tmp_v, motion_line)[1]
ref_motion_column = np.meshgrid(tmp_v, motion_column)[1]
# Matrices with reference values of the motion vectors shifted
# Each image block is a line vector with dx*dy width
shifted_motion_line = np.meshgrid(motion_line, tmp_v)[0]
shifted_motion_column = np.meshgrid(motion_column, tmp_v)[0]
# Sum to calculate the position in rff
# values_line = k + -dy(i) -m2 + dy(l) + rff_center
# Add 1 to account for diferences in indexing between MATLAB and Python
values_lines = inner_ref_m_line - outer_ref_m_line + ref_motion_line - shifted_motion_line + center_line + 1
values_columns = inner_ref_m_column - outer_ref_m_column + ref_motion_column - shifted_motion_column + center_column + 1
# Flatten matrices to vectors
values_lines = mt.vectorize_matrix(values_lines.T)
values_columns = mt.vectorize_matrix(values_columns.T)
# Calculate position considering rff a column vector
positions = (rff.shape[0] * (values_columns - 1)) + values_lines
rff_v = mt.vectorize_matrix(rff)
return np.reshape(rff_v[positions.astype(int) - 1], (k, k))
def _calculate_r(rff, dx, dy, wx, wy, nrows, ncols):
# Center of the matrix - point with maximum value
center_line, center_column = np.unravel_index(rff.argmax(), rff.shape)
# Number of images
p = len(dx)
k = (p * wx * wy) / (nrows * ncols)
# Reference vectors
xv = np.arange(0, wx / nrows) + 1
yv = np.arange(0, wy / ncols) + 1
ref_line, ref_column = np.meshgrid(xv, yv)
ref_line = mt.vectorize_matrix(ref_line)
ref_column = mt.vectorize_matrix(ref_column)
# Initialize matrix
zeros = np.zeros(9)
ref_v_line = mt.generate_and_flatten_grid(zeros, ref_line, 'Y')
ref_v_column = mt.generate_and_flatten_grid(zeros, ref_column, 'Y')
# Inner loop - fill R's columns - line vectors
inner_ref_m_column = np.meshgrid(ref_v_column, ref_v_column)[0] * 3
inner_ref_m_line = np.meshgrid(ref_v_line, ref_v_line)[0] * 3
# Outer loop - fill R's lines - column vectors
outer_ref_m_line = inner_ref_m_line.T
outer_ref_m_column = inner_ref_m_column.T
# Include motion matrices
yv = np.arange(k / p) + 1
motion_line = mt.generate_and_flatten_grid(dy, yv, 'X')
motion_column = mt.generate_and_flatten_grid(dx, yv, 'X')
# Matrices with reference values of the motion vectors
# Each image block is a line vector with dx*dy width
tmp_v = np.arange(k) + 1
ref_motion_line = np.meshgrid(tmp_v, motion_line)[1]
ref_motion_column = np.meshgrid(tmp_v, motion_column)[1]
# Matrices with reference values of the motion vectors shifted
# Each image block is a line vector with dx*dy width
shifted_motion_line = np.meshgrid(motion_line, tmp_v)[0]
shifted_motion_column = np.meshgrid(motion_column, tmp_v)[0]
# Sum to calculate the position in rff
# values_line = k + -dy(i) -m2 + dy(l) + rff_center
# Add 1 to account for diferences in indexing between MATLAB and Python
values_lines = inner_ref_m_line - outer_ref_m_line + ref_motion_line - shifted_motion_line + center_line + 1
values_columns = inner_ref_m_column - outer_ref_m_column + ref_motion_column - shifted_motion_column + center_column + 1
# Flatten matrices to vectors
values_lines = mt.vectorize_matrix(values_lines.T)
values_columns = mt.vectorize_matrix(values_columns.T)
# Calculate position considering rff a column vector
positions = (rff.shape[0] * (values_columns - 1)) + values_lines
rff_v = mt.vectorize_matrix(rff)
return np.reshape(rff_v[positions.astype(int) - 1], (k, k))
def _calculate_p(rdf, dx, dy, wx, wy, nrows, ncols):
# Given an observation matrix (W), calculate the distance between
# its points and the subwindow (D).
# Each column of the P matrix represents a subwindow D.
# Number of images
nimgs = len(dx)
k = (nimgs * wx * wy) / (nrows * ncols)
# Outer loop
# Inner matrix (subwindow) - varies in the lines of the P matrix
m_pos_x = np.meshgrid(
mt.generate_and_flatten_grid(
np.arange(ncols) + 1 - np.fix((ncols + 1) / 2)
),
np.zeros(k)
)[0]
m_pos_y = np.meshgrid(
mt.generate_and_flatten_grid(
np.arange(nrows) + 1 - np.fix((nrows + 1) / 2),
grid='Y'
),
np.zeros(k)
)[0]
tmp_v = np.arange(k/nimgs) + 1
m_dx = np.meshgrid(
np.zeros(ncols * nrows),
mt.generate_and_flatten_grid(dx, tmp_v)
)[1]
m_dy = np.meshgrid(
np.zeros(ncols * nrows),
mt.generate_and_flatten_grid(dy, tmp_v)
)[1]
tmp_v1 = np.zeros(nimgs)
tmp_v2 = np.zeros(ncols * nrows)
m_c_pos_x = np.meshgrid(
tmp_v2,
mt.generate_and_flatten_grid(
tmp_v1, mt.generate_and_flatten_grid(
(np.arange(wx/ncols) + 1 - np.fix((wx/ncols + 1) / 2)) * ncols
),
grid='Y'
)
)[1]
m_c_pos_y = np.meshgrid(
tmp_v2,
mt.generate_and_flatten_grid(
tmp_v1,
mt.generate_and_flatten_grid(
(np.arange(wy/nrows) + 1 - np.fix((wy/nrows + 1) / 2)) * nrows,
grid='Y'
),
grid='Y')
)[1]
# Calculate values for every point
# -m1 + j + 29 - dx(i) -> - inner_window + outer_window
# Add +1 to compensate 0 index matrix
# Center of the matrix - point with maximum value
center_row, center_column = np.unravel_index(rdf.argmax(), rdf.shape)
# TODO is it really the center_row to be added?
val_x = mt.vectorize_matrix((m_c_pos_x - m_dx - m_pos_x + center_row + 1).T)
# TODO is it really the center_column to be added?
val_y = mt.vectorize_matrix((m_c_pos_y - m_dy - m_pos_y + center_column + 1).T)
# Calculate positions using rdf as a vector
# Subtract 1 to normalize to 0 index
positions = (rdf.shape[0] * (val_x - 1) + val_y).astype(int) - 1
rdf_v = mt.vectorize_matrix(rdf)
return np.reshape(rdf_v[positions], (k, nrows * ncols), order='F')
def _calculate_p(rdf, dx, dy, wx, wy, nrows, ncols):
# Given an observation matrix (W), calculate the distance between
# its points and the subwindow (D).
# Each column of the P matrix represents a subwindow D.
# Number of images
nimgs = len(dx)
k = (nimgs * wx * wy) / (nrows * ncols)
# Outer loop
# Inner matrix (subwindow) - varies in the lines of the P matrix
m_pos_x = np.meshgrid(
mt.generate_and_flatten_grid(
np.arange(ncols) + 1 - np.fix((ncols + 1) / 2)), np.zeros(k))[0]
m_pos_y = np.meshgrid(
mt.generate_and_flatten_grid(np.arange(nrows) + 1 - np.fix(
(nrows + 1) / 2),
grid='Y'), np.zeros(k))[0]
tmp_v = np.arange(k / nimgs) + 1
m_dx = np.meshgrid(np.zeros(ncols * nrows),
mt.generate_and_flatten_grid(dx, tmp_v))[1]
m_dy = np.meshgrid(np.zeros(ncols * nrows),
mt.generate_and_flatten_grid(dy, tmp_v))[1]
tmp_v1 = np.zeros(nimgs)
tmp_v2 = np.zeros(ncols * nrows)
m_c_pos_x = np.meshgrid(
tmp_v2,
mt.generate_and_flatten_grid(tmp_v1,
mt.generate_and_flatten_grid(
(np.arange(wx / ncols) + 1 - np.fix(
(wx / ncols + 1) / 2)) * ncols),
grid='Y'))[1]
m_c_pos_y = np.meshgrid(
tmp_v2,
mt.generate_and_flatten_grid(tmp_v1,
mt.generate_and_flatten_grid(
(np.arange(wy / nrows) + 1 - np.fix(
(wy / nrows + 1) / 2)) * nrows,
grid='Y'),
grid='Y'))[1]
# Calculate values for every point
# -m1 + j + 29 - dx(i) -> - inner_window + outer_window
# Add +1 to compensate 0 index matrix
# Center of the matrix - point with maximum value
center_row, center_column = np.unravel_index(rdf.argmax(), rdf.shape)
# TODO is it really the center_row to be added?
val_x = mt.vectorize_matrix(
(m_c_pos_x - m_dx - m_pos_x + center_row + 1).T)
# TODO is it really the center_column to be added?
val_y = mt.vectorize_matrix(
(m_c_pos_y - m_dy - m_pos_y + center_column + 1).T)
# Calculate positions using rdf as a vector
# Subtract 1 to normalize to 0 index
positions = (rdf.shape[0] * (val_x - 1) + val_y).astype(int) - 1
rdf_v = mt.vectorize_matrix(rdf)
return np.reshape(rdf_v[positions], (k, nrows * ncols), order='F')