Homogeneous Transforms



In [1]:

    
import numpy as np

from menpo.shape import PointCloud
from menpo.transform import Homogeneous

If you know the form of a basic homogeneous transform (like here a mirror along y=x) it's trivial to build a Homogeneous to use this operation in Menpo



In [2]:

    
# mirror along y=x
xy_yx = Homogeneous(np.array([[0, 1, 0], 
                              [1, 0, 0], 
                              [0, 0, 1]]))



In [3]:

    
s = np.linspace(0, 1)
len(s)
p = np.ones([len(s), 2])
p[:, 1] = s
pc = PointCloud(p)
print(pc)









    



PointCloud: n_points: 50, n_dims: 2



In [4]:

    
%matplotlib inline
pc.view(axes_y_limits=(0.5, 1.5));

Let's take a look at what our homogeneous transform is exactly



In [5]:

    
print(xy_yx)









    



Homogeneous
[[0 1 0]
 [1 0 0]
 [0 0 1]]

Applying this Transform to a PointCloud has the desired effect



In [6]:

    
pc_flipped = xy_yx.apply(pc)



In [7]:

    
pc_flipped.view(axes_x_limits=(0.5, 1.5));

Homogeneous transforms support native composition



In [8]:

    
no_op = xy_yx.compose_before(xy_yx)
print(no_op)









    



Homogeneous
[[1 0 0]
 [0 1 0]
 [0 0 1]]



In [9]:

    
no_op = xy_yx.compose_after(xy_yx)
print(no_op)









    



Homogeneous
[[1 0 0]
 [0 1 0]
 [0 0 1]]



In [10]:

    
xy_yx.compose_before_inplace(xy_yx)
print(xy_yx)









    



Homogeneous
[[1 0 0]
 [0 1 0]
 [0 0 1]]