def similarity_transform_matr(points):
f_points_count = float(len(points))
xi, yi = lu.unzip(points)
mean_x = lu.mean(xi)
mean_y = lu.mean(yi)
distances = map(lambda (x, y): math.sqrt((x-mean_x)**2 + (y-mean_y)**2),
zip(xi, yi))
avg_dist = sum(distances)/f_points_count
s = f_points_count*math.sqrt(2.0)/avg_dist
tx, ty = -s*mean_x, -s*mean_y
return np.array([[ s, 0.0, tx],
[0.0, s, ty],
[0.0, 0.0, 1.0]])
def normalized_dlt(match_list):
"""
Calculates a homography using Direct Linear Transformation algorithm, normalizing
image point sets independently.
match_list: a list of point matches
[[(x1, y1), (x1', y1')], [(x2, y2), (x2', y2')], ...]
"""
if logger.isEnabledFor(DEBUG):
logger.debug('Normalized DLT started: match list = %s', match_list)
points1, points2 = lu.unzip(match_list)
if logger.isEnabledFor(DEBUG):
logger.debug('\nPoints1 =\n%s\nPoints2 =\n%s', points1, points2)
T1 = similarity_transform_matr(points1)
T2 = similarity_transform_matr(points2)
hg_points1 = pt.list_to_homogeneous(points1)
hg_points2 = pt.list_to_homogeneous(points2)
hg_points1 = np.dot(T1, np.array(hg_points1).T).T
hg_points2 = np.dot(T2, np.array(hg_points2).T).T
points1 = pt.ndarray2d_to_list(hg_points1)
points2 = pt.ndarray2d_to_list(hg_points2)
if logger.isEnabledFor(DEBUG):
logger.debug('\nPoints1 =\n%s\nPoints2 =\n%s', points1, points2)
points1 = pt.list_to_cartesian(points1)
points2 = pt.list_to_cartesian(points2)
normalized_points = zip(points1, points2)
if logger.isEnabledFor(DEBUG):
logger.debug('\nNormalized points: %s', normalized_points)
H = dlt(normalized_points)
return np.dot(np.linalg.inv(T2), np.dot(H, T1))
