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# --*-- coding:utf-8 --*--
import numpy as np
import cv2
from scipy import signal
'''
helper function
'''
def filterItChopOff(f, r, sp):
f[np.isnan(f)] = 0
H, W, d = f.shape
B = np.ones([2 * r + 1, 2 * r + 1]) # 2r+1 * 2r+1 neighbourhood
minSP = cv2.erode(sp, B, iterations=1)
maxSP = cv2.dilate(sp, B, iterations=1)
ind = np.where(np.logical_or(minSP != sp, maxSP != sp))
spInd = np.reshape(range(np.size(sp)), sp.shape,'F')
delta = np.zeros(f.shape)
delta = np.reshape(delta, (H * W, d), 'F')
f = np.reshape(f, (H * W, d),'F')
# calculate delta
I, J = np.unravel_index(ind, [H, W], 'C')
for i in range(np.size(ind)):
x = I[i]
y = J[i]
clipInd = spInd[max(0, x - r):min(H-1, x + r), max(0, y - r):min(W-1, y + r)]
diffInd = clipInd[sp[clipInd] != sp[x, y]]
delta[ind[i], :] = np.sum(f[diffInd, :], 1)
delta = np.reshape(delta, (H, W, d), 'F')
f = np.reshape(f, (H, W, d), 'F')
fFilt = np.zeros([H, W, d])
for i in range(f.shape[2]):
# fFilt(:,:,i) = filter2(B, f(:,:,i));
tmp = cv2.filter2D(np.rot90(f[:, :, i], 2), -1, np.rot90(np.rot90(B, 2), 2))
tmp = signal.convolve2d(np.rot90(f[:, :, i], 2), np.rot90(np.rot90(B, 2), 2), mode="same")
fFilt[:, :, i] = np.rot90(tmp, 2)
fFilt = fFilt - delta
return fFilt
'''
helper function
'''
def mutiplyIt(AtA_1, Atb):
result = np.zeros([Atb.shape[0], Atb.shape[1], 3])
result[:, :, 0] = np.multiply(AtA_1[:, :, 0], Atb[:, :, 0]) + np.multiply(AtA_1[:, :, 1],
Atb[:, :, 1]) + np.multiply(
AtA_1[:, :, 2], Atb[:, :, 2])
result[:, :, 1] = np.multiply(AtA_1[:, :, 1], Atb[:, :, 0]) + np.multiply(AtA_1[:, :, 3],
Atb[:, :, 1]) + np.multiply(
AtA_1[:, :, 4], Atb[:, :, 2])
result[:, :, 2] = np.multiply(AtA_1[:, :, 2], Atb[:, :, 0]) + np.multiply(AtA_1[:, :, 4],
Atb[:, :, 1]) + np.multiply(
AtA_1[:, :, 5], Atb[:, :, 2])
return result
'''
helper function
'''
def invertIt(AtA):
AtA_1 = np.zeros([AtA.shape[0], AtA.shape[1], 6])
AtA_1[:, :, 0] = np.multiply(AtA[:, :, 3], AtA[:, :, 5]) - np.multiply(AtA[:, :, 4], AtA[:, :, 4])
AtA_1[:, :, 1] = -np.multiply(AtA[:, :, 1], AtA[:, :, 5]) + np.multiply(AtA[:, :, 2], AtA[:, :, 4])
AtA_1[:, :, 2] = np.multiply(AtA[:, :, 1], AtA[:, :, 4]) - np.multiply(AtA[:, :, 2], AtA[:, :, 3])
AtA_1[:, :, 3] = np.multiply(AtA[:, :, 0], AtA[:, :, 5]) - np.multiply(AtA[:, :, 2], AtA[:, :, 2])
AtA_1[:, :, 4] = -np.multiply(AtA[:, :, 0], AtA[:, :, 4]) + np.multiply(AtA[:, :, 1], AtA[:, :, 2])
AtA_1[:, :, 5] = np.multiply(AtA[:, :, 0], AtA[:, :, 3]) - np.multiply(AtA[:, :, 1], AtA[:, :, 1])
x1 = np.multiply(AtA[:, :, 0], AtA_1[:, :, 0])
x2 = np.multiply(AtA[:, :, 1], AtA_1[:, :, 1])
x3 = np.multiply(AtA[:, :, 2], AtA_1[:, :, 2])
detAta = x1 + x2 + x3
return AtA_1, detAta
'''
Compute the direction of gravity
N: normal field
iter: number of 'big' iterations
'''
def getYDir(N, angleThresh, iter, y0):
y = y0
for i in range(len(angleThresh)):
thresh = np.pi * angleThresh[i] / 180 # convert it to radian measure
y = getYDirHelper(N, y, thresh, iter[i])
return y
'''
N: HxWx3 matrix with normal at each pixel.
y0: the initial gravity direction
thresh: in degrees the threshold for mapping to parallel to gravity and perpendicular to gravity
iter: number of iterations to perform
'''
def getYDirHelper(N, y0, thresh, num_iter):
dim = N.shape[0] * N.shape[1]
# change the third dimension to the first-order. (480, 680, 3) => (3, 480, 680)
nn = np.swapaxes(np.swapaxes(N,0,2),1,2)
nn = np.reshape(nn, (3, dim), 'F')
# remove these whose number is NAN
idx = np.where(np.invert(np.isnan(nn[0,:])))[0]
nn = nn[:,idx]
# Set it up as a optimization problem
yDir = y0;
for i in range(num_iter):
sim0 = np.dot(yDir.T, nn)
indF = abs(sim0) > np.cos(thresh) # calculate 'floor' set. |sin(theta)| < sin(thresh) ==> |cos(theta)| > cos(thresh)
indW = abs(sim0) < np.sin(thresh) # calculate 'wall' set.
if(len(indF.shape) == 2):
NF = nn[:, indF[0,:]]
NW = nn[:, indW[0,:]]
else:
NF = nn[:, indF]
NW = nn[:, indW]
A = np.dot(NW, NW.T) - np.dot(NF, NF.T)
b = np.zeros([3,1])
c = NF.shape[1]
w,v = np.linalg.eig(A) # w:eigenvalues; v:eigenvectors
min_ind = np.argmin(w) # min index
newYDir = v[:,min_ind]
yDir = newYDir * np.sign(np.dot(yDir.T, newYDir))
return yDir
'''
getRMatrix: Generate a rotation matrix that
if yf is a scalar, rotates about axis yi by yf degrees
if yf is an axis, rotates yi to yf in the direction given by yi x yf
Input: yi is an axis 3x1 vector
yf could be a scalar of axis
'''
# def getRMatrix(yi, yf):
# if (np.isscalar(yf)):
# ax = yi / np.linalg.norm(yi) # norm(A) = max(svd(A))
# phi = yf
# else:
# yi = yi / np.linalg.norm(yi)
# yf = yf / np.linalg.norm(yf)
# ax = np.cross(yi.T, yf.T).T
# ax = ax / np.linalg.norm(ax)
# # find angle of rotation
# phi = np.degrees(np.arccos(np.dot(yi.T, yf)))
# if (abs(phi) > 0.1):
# phi = phi * (np.pi / 180)
# s_hat = np.array([[0, -ax[2], ax[1]],
# [ax[2], 0, -ax[0]],
# [-ax[1], ax[0], 0]])
# R = np.eye(3) + np.sin(phi) * s_hat + (1 - np.cos(phi)) * np.dot(s_hat, s_hat) # dot???
# else:
# R = np.eye(3)
# return R
def getRMatrix(yi, yf):
if (np.isscalar(yf)):
ax = yi / np.linalg.norm(yi) # norm(A) = max(svd(A))
phi = yf
else:
yi = yi / np.linalg.norm(yi)
yf = yf / np.linalg.norm(yf)
ax = np.cross(yi.T, yf.T).T
ax = ax / np.linalg.norm(ax)
# find angle of rotation
phi = np.degrees(np.arccos(np.dot(yi.T, yf)))
ax = np.squeeze(ax, axis=-1)
if (abs(phi) > 0.1):
phi = phi * (np.pi / 180)
s_hat = np.array([[0, -ax[2], ax[1]],
[ax[2], 0, -ax[0]],
[-ax[1], ax[0], 0]], dtype=np.float64)
R = np.eye(3) + np.sin(phi) * s_hat + (1 - np.cos(phi)) * np.dot(s_hat, s_hat) # dot???
else:
R = np.eye(3)
return R
'''
Calibration of gravity direction
'''
def rotatePC(pc, R):
if(np.array_equal(R, np.eye(3))):
return pc
else:
R = R.astype(np.float64)
dim = pc.shape[0] * pc.shape[1]
pc = np.swapaxes(np.swapaxes(pc, 0, 2), 1, 2)
res = np.reshape(pc, (3, dim), 'F')
res = np.dot(R, res)
res = np.reshape(res, pc.shape, 'F')
res = np.swapaxes(np.swapaxes(res, 0, 1), 1, 2)
return res |