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flowtools.py
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flowtools.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Feb 4 16:31:45 2015
@author: gottfried
"""
import numpy as np
from PyQt4 import QtGui
import scipy.sparse as sparse
from scipy import ndimage
from matplotlib.backends.backend_qt4agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.backends.backend_qt4agg import NavigationToolbar2QT as NavigationToolbar
from matplotlib.figure import Figure
class MplWidget(QtGui.QWidget):
def __init__(self, parent=None):
super(MplWidget, self).__init__(parent)
self.figure = Figure()
self.ax = self.figure.add_subplot(111)
self.canvas = FigureCanvas(self.figure)
self.toolbar = NavigationToolbar(self.canvas, self)
layout = QtGui.QVBoxLayout()
layout.addWidget(self.toolbar)
layout.addWidget(self.canvas)
self.setLayout(layout)
self.cb = None
self.im = None
self.imsz = None
def imshow(self, img):
if self.im:
self.imsz = self.im.get_size()
newsz = img.shape
self.im.set_data(img)
if self.imsz[0] != newsz[0] or self.imsz[1] != newsz[1]: # update extent
self.im.set_extent((-0.5, newsz[1]-0.5, newsz[0]-0.5, -0.5))
else:
self.im = self.ax.imshow(img,interpolation='none')
if self.cb:
self.im.autoscale()
else:
self.cb = self.figure.colorbar(self.im)
report_pixel = lambda x, y : "(%6.3f, %6.3f) %.3f" % (x,y, img[np.floor(y+0.5),np.floor(x+0.5)])
self.ax.format_coord = report_pixel
self.canvas.draw()
self.canvas.flush_events()
def imresize(img, sz):
"""
Resize image
Input:
img: A grayscale image
sz: A tuple with the new size (rows, cols)
Output:
Ir: Resized image
"""
if np.all(img.shape==sz):
return img;
factors = (np.array(sz)).astype('f') / (np.array(img.shape)).astype('f')
if np.any(factors < 1): # smooth before downsampling
sigmas = (1.0/factors)/3.0
#print img.shape, sz, sigmas
I_filter = ndimage.filters.gaussian_filter(img,sigmas)
else:
I_filter = img
u,v = np.meshgrid(np.arange(0,sz[1]).astype('f'), np.arange(0,sz[0]).astype('f'))
fx = (float(img.shape[1])) / (sz[1]) # multiplicative factors mapping new coords -> old coords
fy = (float(img.shape[0])) / (sz[0])
u *= fx; u += (1.0/factors[1])/2 - 1 + 0.5 # sample from correct position
v *= fy; v += (1.0/factors[0])/2 - 1 + 0.5
# bilinear interpolation
Ir = ndimage.map_coordinates(I_filter, np.vstack((v.flatten().transpose(),u.flatten().transpose())), order=1, mode='nearest')
Ir = np.reshape(Ir, (sz[0], sz[1]))
return Ir
def backproject(shape, K):
x,y = np.meshgrid(np.arange(0, shape[1]), np.arange(0, shape[0]))
fx = K[0,0]; fy = K[1,1]; cx = K[0,2]; cy = K[1,2]
Xn = np.ones((3, x.size))
Xn[0,:] = (x.flatten() - cx) / fx
Xn[1,:] = (y.flatten() - cy) / fy
return Xn
def relative_transformation(G0, G1):
G01 = np.zeros((3,4))
G01[0:3,0:3] = np.dot(G1[0:3,0:3], G0[0:3,0:3].transpose())
G01[0:3,3] = G1[0:3,3] - np.dot(G01[0:3,0:3], G0[0:3,3])
return G01
def make_derivatives_2D_complete(shape):
r"""
Sparse matrix approximation of gradient operator on image plane.
Use forward differences inside image, backward differences at left/bottom border
:param shape: image size (tuple of ints)
Returns:
:Kx,Ky: sparse matrices for gradient in x- and y-direction
"""
M = shape[0]
N = shape[1]
x,y = np.meshgrid(np.arange(0,N), np.arange(0,M))
linIdx = np.ravel_multi_index((y,x), x.shape) # linIdx[y,x] = linear index of (x,y) in an array of size MxN
i = np.vstack( (np.reshape(linIdx[:,:-1], (-1,1) ), np.reshape(linIdx[:,:-1], (-1,1) )) ) # row indices
j = np.vstack( (np.reshape(linIdx[:,:-1], (-1,1) ), np.reshape(linIdx[:,1:], (-1,1) )) ) # column indices
v = np.vstack( (np.ones( (M*(N-1),1) )*-1, np.ones( (M*(N-1),1) )) ) # values
i = np.vstack( (i, np.reshape(linIdx[:,-1], (-1,1) ), np.reshape(linIdx[:,-1], (-1,1) )) ) # row indices
j = np.vstack( (j, np.reshape(linIdx[:,-1], (-1,1) ), np.reshape(linIdx[:,-2], (-1,1) )) ) # column indices
v = np.vstack( (v, np.ones( ((M),1) )*1, np.ones( ((M),1) )*-1) ) # values
Kx = sparse.coo_matrix((v.flatten(),(i.flatten(),j.flatten())), shape=(M*N,M*N))
i = np.vstack( (np.reshape(linIdx[:-1,:], (-1,1) ), np.reshape(linIdx[:-1,:], (-1,1) )) )
j = np.vstack( (np.reshape(linIdx[:-1,:], (-1,1) ), np.reshape(linIdx[1:,:], (-1,1) )) )
v = np.vstack( (np.ones( ((M-1)*N,1) )*-1, np.ones( ((M-1)*N,1) )) )
i = np.vstack( (i, np.reshape(linIdx[-1,:], (-1,1) ), np.reshape(linIdx[-1,:], (-1,1) )) )
j = np.vstack( (j, np.reshape(linIdx[-1,:], (-1,1) ), np.reshape(linIdx[-2,:], (-1,1) )) )
v = np.vstack( (v, np.ones( ((N),1) )*1, np.ones( ((N),1) )*-1) )
Ky = sparse.coo_matrix((v.flatten(),(i.flatten(),j.flatten())), shape=(M*N,M*N))
return Kx.tocsr(),Ky.tocsr()
def make_linearOperator(shape, Xn, K):
M,N = shape
fx = K[0,0]
fy = K[1,1]
x_hat = Xn[0,:]
y_hat = Xn[1,:]
Kx,Ky = make_derivatives_2D_complete(shape) # use one-sided differences with backward diff at image border
Kx = Kx.tocsr()
Ky = Ky.tocsr()
spId = sparse.eye(M*N, M*N, format='csr')
spXhat = sparse.diags(x_hat.flatten(), 0).tocsr()
spYhat = sparse.diags(y_hat.flatten(), 0).tocsr()
L = sparse.vstack([-Kx/fy, -Ky/fx,
spXhat*Kx/fy + spYhat*Ky/fx +
2*spId/(fx*fy)
])
return L.tocsr()
def to_zeta(z):
return (z**2) / 2
def to_z(zeta):
return np.sqrt(2*zeta)
def huber_function(data, epsilon):
idx1 = np.where(np.abs(data)>=epsilon); idx2 = np.where(np.abs(data)<epsilon)
result = np.zeros(data.shape)
result[idx1] = np.abs(data[idx1])-0.5*epsilon
result[idx2] = np.abs(data[idx2])**2/(2*epsilon)
return result
def camera_baseline(G0, G1):
p0 = np.dot(-G0[0:3,0:3].T, G0[0:3,3])
p1 = np.dot(-G1[0:3,0:3].T, G1[0:3,3])
return np.linalg.norm(p0-p1)