Intensity Values

Biomedical Image Analysis in Python

Stephen Bailey

Instructor

Pixels and voxels

Pixels are 2D picture elements
Voxels are 3D volume elements
Two properties: intensity and location

foot-xray

Data types and image size

Array's data type controls range of possible intensities

Type	Range	No. Val.
uint8	0, 255	256
int8	- 128, 127	256
uint16	0, 2$^{16}$	2$^{16}$
int16	-2$^{15}$, 2$^{15}$	2$^{16}$
float16	~-2$^{16}$, ~2$^{16}$	>>2$^{16}$

import imageio

im=imageio.imread('foot-xray.jpg')

im.dtype
    dtype('uint8')

im.size

im_int64 = im.astype(np.uint64)
im_int64.size

Histograms

Histograms: count number of pixels at each intensity value.
Implemented in scipy.ndimage
- higher-dimensional arrays
- masked data
Advanced techniques and functionality in scikit-image.

plt.plot(hist)
plt.show()

import scipy.ndimage as ndi

hist=ndi.histogram(im, min=0, 
                       max=255,
                       bins=256)

hist.shape

(256,)

Histogram

Equalization

Distributions often skewed toward low intensities (background values).
Equalization: redistribute values to optimize full intensity range.
Cumulative distribution function: (CDF) shows proportion of pixels in range.

Hist+CDF

Equalization

import scipy.ndimage as ndi
hist = ndi.histogram(im, min=0, 
                         max=255,
                        bins=256)

cdf = hist.cumsum() / hist.sum()
cdf.shape

(256,)

im_equalized = cdf[im] * 255

fig, axes = plt.subplots(2, 1)
axes[0].imshow(im)
axes[1].imshow(im_equalized)
plt.show()

equalized-image

Let's practice!

Biomedical Image Analysis in Python