ref: d55682c2aadbca664727fde886d42d39f7cbb5cd
dir: libvpx/tools/3D-Reconstruction/MotionEST/Anandan.py
## Copyright (c) 2020 The WebM project authors. All Rights Reserved.
##
## Use of this source code is governed by a BSD-style license
## that can be found in the LICENSE file in the root of the source
## tree. An additional intellectual property rights grant can be found
## in the file PATENTS. All contributing project authors may
## be found in the AUTHORS file in the root of the source tree.
##
# coding: utf-8
import numpy as np
import numpy.linalg as LA
from scipy.ndimage.filters import gaussian_filter
from scipy.sparse import csc_matrix
from scipy.sparse.linalg import inv
from MotionEST import MotionEST
"""Anandan Model"""
class Anandan(MotionEST):
"""
constructor:
cur_f: current frame
ref_f: reference frame
blk_sz: block size
beta: smooth constrain weight
k1,k2,k3: confidence coefficients
max_iter: maximum number of iterations
"""
def __init__(self, cur_f, ref_f, blk_sz, beta, k1, k2, k3, max_iter=100):
super(Anandan, self).__init__(cur_f, ref_f, blk_sz)
self.levels = int(np.log2(blk_sz))
self.intensity_hierarchy()
self.c_maxs = []
self.c_mins = []
self.e_maxs = []
self.e_mins = []
for l in xrange(self.levels + 1):
c_max, c_min, e_max, e_min = self.get_curvature(self.cur_Is[l])
self.c_maxs.append(c_max)
self.c_mins.append(c_min)
self.e_maxs.append(e_max)
self.e_mins.append(e_min)
self.beta = beta
self.k1, self.k2, self.k3 = k1, k2, k3
self.max_iter = max_iter
"""
build intensity hierarchy
"""
def intensity_hierarchy(self):
level = 0
self.cur_Is = []
self.ref_Is = []
#build each level itensity by using gaussian filters
while level <= self.levels:
cur_I = gaussian_filter(self.cur_yuv[:, :, 0], sigma=(2**level) * 0.56)
ref_I = gaussian_filter(self.ref_yuv[:, :, 0], sigma=(2**level) * 0.56)
self.ref_Is.append(ref_I)
self.cur_Is.append(cur_I)
level += 1
"""
get curvature of each block
"""
def get_curvature(self, I):
c_max = np.zeros((self.num_row, self.num_col))
c_min = np.zeros((self.num_row, self.num_col))
e_max = np.zeros((self.num_row, self.num_col, 2))
e_min = np.zeros((self.num_row, self.num_col, 2))
for r in xrange(self.num_row):
for c in xrange(self.num_col):
h11, h12, h21, h22 = 0, 0, 0, 0
for i in xrange(r * self.blk_sz, r * self.blk_sz + self.blk_sz):
for j in xrange(c * self.blk_sz, c * self.blk_sz + self.blk_sz):
if 0 <= i < self.height - 1 and 0 <= j < self.width - 1:
Ix = I[i][j + 1] - I[i][j]
Iy = I[i + 1][j] - I[i][j]
h11 += Iy * Iy
h12 += Ix * Iy
h21 += Ix * Iy
h22 += Ix * Ix
U, S, _ = LA.svd(np.array([[h11, h12], [h21, h22]]))
c_max[r, c], c_min[r, c] = S[0], S[1]
e_max[r, c] = U[:, 0]
e_min[r, c] = U[:, 1]
return c_max, c_min, e_max, e_min
"""
get ssd of motion vector:
cur_I: current intensity
ref_I: reference intensity
center: current position
mv: motion vector
"""
def get_ssd(self, cur_I, ref_I, center, mv):
ssd = 0
for r in xrange(int(center[0]), int(center[0]) + self.blk_sz):
for c in xrange(int(center[1]), int(center[1]) + self.blk_sz):
if 0 <= r < self.height and 0 <= c < self.width:
tr, tc = r + int(mv[0]), c + int(mv[1])
if 0 <= tr < self.height and 0 <= tc < self.width:
ssd += (ref_I[tr, tc] - cur_I[r, c])**2
else:
ssd += cur_I[r, c]**2
return ssd
"""
get region match of level l
l: current level
last_mvs: matchine results of last level
radius: movenment radius
"""
def region_match(self, l, last_mvs, radius):
mvs = np.zeros((self.num_row, self.num_col, 2))
min_ssds = np.zeros((self.num_row, self.num_col))
for r in xrange(self.num_row):
for c in xrange(self.num_col):
center = np.array([r * self.blk_sz, c * self.blk_sz])
#use overlap hierarchy policy
init_mvs = []
if last_mvs is None:
init_mvs = [np.array([0, 0])]
else:
for i, j in {(r, c), (r, c + 1), (r + 1, c), (r + 1, c + 1)}:
if 0 <= i < last_mvs.shape[0] and 0 <= j < last_mvs.shape[1]:
init_mvs.append(last_mvs[i, j])
#use last matching results as the start position as current level
min_ssd = None
min_mv = None
for init_mv in init_mvs:
for i in xrange(-2, 3):
for j in xrange(-2, 3):
mv = init_mv + np.array([i, j]) * radius
ssd = self.get_ssd(self.cur_Is[l], self.ref_Is[l], center, mv)
if min_ssd is None or ssd < min_ssd:
min_ssd = ssd
min_mv = mv
min_ssds[r, c] = min_ssd
mvs[r, c] = min_mv
return mvs, min_ssds
"""
smooth motion field based on neighbor constraint
uvs: current estimation
mvs: matching results
min_ssds: minimum ssd of matching results
l: current level
"""
def smooth(self, uvs, mvs, min_ssds, l):
sm_uvs = np.zeros((self.num_row, self.num_col, 2))
c_max = self.c_maxs[l]
c_min = self.c_mins[l]
e_max = self.e_maxs[l]
e_min = self.e_mins[l]
for r in xrange(self.num_row):
for c in xrange(self.num_col):
w_max = c_max[r, c] / (
self.k1 + self.k2 * min_ssds[r, c] + self.k3 * c_max[r, c])
w_min = c_min[r, c] / (
self.k1 + self.k2 * min_ssds[r, c] + self.k3 * c_min[r, c])
w = w_max * w_min / (w_max + w_min + 1e-6)
if w < 0:
w = 0
avg_uv = np.array([0.0, 0.0])
for i, j in {(r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)}:
if 0 <= i < self.num_row and 0 <= j < self.num_col:
avg_uv += 0.25 * uvs[i, j]
sm_uvs[r, c] = (w * w * mvs[r, c] + self.beta * avg_uv) / (
self.beta + w * w)
return sm_uvs
"""
motion field estimation
"""
def motion_field_estimation(self):
last_mvs = None
for l in xrange(self.levels, -1, -1):
mvs, min_ssds = self.region_match(l, last_mvs, 2**l)
uvs = np.zeros(mvs.shape)
for _ in xrange(self.max_iter):
uvs = self.smooth(uvs, mvs, min_ssds, l)
last_mvs = uvs
for r in xrange(self.num_row):
for c in xrange(self.num_col):
self.mf[r, c] = uvs[r, c]