ref: 7f73dee0e5e0e6bdd2fe1f9718541c7cee455be7
parent: e2d0e7fe01984a7fb57fee11a44d57a051a2c464
author: Dan Zhu <zxdan@google.com>
date: Thu Aug 22 14:20:38 EDT 2019
Add Anandan model Change-Id: Ic3450125c83b41e7e4a953093b4d8177f04d220a
--- /dev/null
+++ b/tools/3D-Reconstruction/MotionEST/Anandan.py
@@ -1,0 +1,185 @@
+#!/usr/bin/env python
+# 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 postion 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]