A crash course on NumPy for images

A crash course on NumPy for images

Images manipulated by scikit-image are simply NumPy arrays. Hence, a large fraction of operations on images will just consist in using NumPy:

>>> from skimage import data
>>> camera = data.camera()
>>> type(camera)
<type 'numpy.ndarray'>

Retrieving the geometry of the image and the number of pixels:

>>> camera.shape
(512, 512)
>>> camera.size
262144

Retrieving statistical information about gray values:

>>> camera.min(), camera.max()
(0, 255)
>>> camera.mean()
118.31400299072266

NumPy arrays representing images can be of different integer of float numerical types. See Image data types and what they mean for more information about these types and how scikit-image treats them.

NumPy indexing can be used both for looking at pixel values, and to modify pixel values:

>>> # Get the value of the pixel on the 10th row and 20th column
>>> camera[10, 20]
153
>>> # Set to black the pixel on the 3rd row and 10th column
>>> camera[3, 10] = 0

Be careful: in NumPy indexing, the first dimension (camera.shape[0]) corresponds to rows, while the second (camera.shape[1]) corresponds to columns, with the origin (camera[0, 0]) on the top-left corner. This matches matrix/linear algebra notation, but is in contrast to Cartesian (x, y) coordinates. See Coordinate conventions below for more details.

Beyond individual pixels, it is possible to access / modify values of whole sets of pixels, using the different indexing possibilities of NumPy.

Slicing:

>>> # Set to black the ten first lines
>>> camera[:10] = 0

Masking (indexing with masks of booleans):

>>> mask = camera < 87
>>> # Set to "white" (255) pixels where mask is True
>>> camera[mask] = 255

Fancy indexing (indexing with sets of indices)

>>> inds_r = np.arange(len(camera))
>>> inds_c = 4 * inds_r % len(camera)
>>> camera[inds_r, inds_c] = 0

Using masks, especially, is very useful to select a set of pixels on which to perform further manipulations. The mask can be any boolean array of same shape as the image (or a shape broadcastable to the image shape). This can be useful to define a region of interest, such as a disk:

>>> nrows, ncols = camera.shape
>>> row, col = np.ogrid[:nrows, :ncols]
>>> cnt_row, cnt_col = nrows / 2, ncols / 2
>>> outer_disk_mask = ((row - cnt_row)**2 + (col - cnt_col)**2 >
...                    (nrows / 2)**2)
>>> camera[outer_disk_mask] = 0

Boolean arithmetic can be used to define more complex masks:

>>> lower_half = row > cnt_row
>>> lower_half_disk = np.logical_and(lower_half, outer_disk_mask)
>>> camera = data.camera()
>>> camera[lower_half_disk] = 0

Color images

All of the above is true of color images, too: a color image is a NumPy array, with an additional trailing dimension for the channels:

>>> cat = data.chelsea()
>>> type(cat)
<type 'numpy.ndarray'>
>>> cat.shape
(300, 451, 3)

This shows that cat is a 300-by-451 pixel image with three channels (red, green, and blue). As before, we can get and set pixel values:

>>> cat[10, 20]
array([151, 129, 115], dtype=uint8)
>>> # set the pixel at row 50, column 60 to black
>>> cat[50, 60] = 0
>>> # set the pixel at row 50, column 61 to green
>>> cat[50, 61] = [0, 255, 0] # [red, green, blue]

We can also use 2D boolean masks for a 2D color image, as we did with the grayscale image above:

Using a 2D mask on a 2D color image

>>> from skimage import data
>>> cat = data.chelsea()
>>> reddish = cat[:, :, 0] > 160
>>> cat[reddish] = [0, 255, 0]
>>> plt.imshow(cat)

(Source code, png, pdf)

Coordinate conventions

Because we represent images with numpy arrays, our coordinates must match accordingly. Two-dimensional (2D) grayscale images (such as camera above) are indexed by row and columns (abbreviated to either row, col or r, c), with the lowest element (0, 0) at the top- -left corner. In various parts of the library, you will also see rr and cc refer to lists of row and column coordinates. We distinguish this from (x, y), which commonly denote standard Cartesian coordinates, where x is the horizontal coordinate, y the vertical, and the origin is on the bottom right. (Matplotlib, for example, uses this convention.)

In the case of color (or multichannel) images, the last dimension contains the color information and is denoted channel or ch.

Finally, for 3D images, such as videos, magnetic resonance imaging (MRI) scans, or confocal microscopy, we refer to the leading dimension as plane, abbreviated as pln or p.

These conventions are summarized below:

Dimension name and order conventions in scikit-image

Image type	coordinates
2D grayscale	(row, col)
2D multichannel (eg. RGB)	(row, col, ch)
3D grayscale	(pln, row, col)
3D multichannel	(pln, row, col, ch)

Many functions in scikit-image operate on 3D images directly:

>>> im3d = np.random.rand(100, 1000, 1000)
>>> from skimage import morphology
>>> from scipy import ndimage as ndi
>>> seeds = ndi.label(im3d < 0.1)[0]
>>> ws = morphology.watershed(im3d, seeds)

In many cases, the third imaging dimension has lower resolution than the other two. Some scikit-image functions provide a spacing keyword argument to process these images:

>>> from skimage import segmentation
>>> slics = segmentation.slic(im3d, spacing=[5, 1, 1], multichannel=False)

Other times, processing must be done plane-wise. When planes are the leading dimension, we can use the following syntax:

>>> from skimage import filters
>>> edges = np.zeros_like(im3d)
>>> for pln, image in enumerate(im3d):
...     # iterate over the leading dimension (planes)
...     edges[pln] = filters.sobel(image)

Notes on array order

Although the labeling of the axes seems arbitrary, it can have a significant effect on speed of operations. This is because modern processors never retrieve just one item from memory, but rather a whole chunk of adjacent items. (This is called prefetching.) Therefore, processing elements that are next to each other in memory is faster than processing them in a different order, even if the number of operations is the same:

>>> def in_order_multiply(arr, scalar):
...     for plane in list(range(arr.shape[0])):
...         arr[plane, :, :] *= scalar
...
>>> def out_of_order_multiply(arr, scalar):
...     for plane in list(range(arr.shape[2])):
...         arr[:, :, plane] *= scalar
...
>>> import time
>>> im3d = np.random.rand(100, 1024, 1024)
>>> t0 = time.time(); x = in_order_multiply(im3d, 5); t1 = time.time()
>>> print("%.2f seconds" % (t1 - t0))  
0.14 seconds
>>> im3d_t = np.transpose(im3d).copy() # place "planes" dimension at end
>>> im3d_t.shape
(1024, 1024, 100)
>>> s0 = time.time(); x = out_of_order_multiply(im3d, 5); s1 = time.time()
>>> print("%.2f seconds" % (s1 - s0))  
1.18 seconds
>>> print("Speedup: %.1fx" % ((s1 - s0) / (t1 - t0)))  
Speedup: 8.6x

When the dimension you are iterating over is even larger, the speedup is even more dramatic. It is worth thinking about this data locality when writing algorithms. In particular, know that scikit-image uses C-contiguous arrays unless otherwise specified, so one should iterate along the last/rightmost dimension in the innermost loop of the computation.

A note on time

Although scikit-image does not currently (0.11) provide functions to work specifically with time-varying 3D data, our compatibility with numpy arrays allows us to work quite naturally with a 5D array of the shape (t, pln, row, col, ch):

>>> for timepoint in image5d:  
...     # each timepoint is a 3D multichannel image
...     do_something_with(timepoint)

We can then supplement the above table as follows:

Addendum to dimension names and orders in scikit-image

Image type	coordinates
2D color video	(t, row, col, ch)
3D multichannel video	(t, pln, row, col, ch)