Image Properties and Simple Point
Operations
CS/BIOEN 4640: Image Processing Basics
January 17, 2012
Image Brightness
Definition
The brightness of a grayscale image is the average
over all pixel intensities.
So, the equation for brightness of an image I is
h
w
1 XX
B(I) =
I(u, v)
wh
v=1 u=1
Dynamic Range
Definition
The dynamic range of an image is the total number of
distinctive pixel values that occur in the image.
I
Dynamic range is limited by the number of bits per
pixel used to represent the image.
I
Also limited by the dynamic range of the sensor.
I
Image processing cannot add dynamic range
(without making it up).
Example: Dynamic Range
Very Low Dynamic
Range (6 values)
Low Dynamic
Range (64 values)
High Dynamic
Range
High Dynamic Range Imaging
I
If both dark and bright areas in a scene, a camera
cannot capture details in them both with a single
exposure.
I
Details in dark areas are captured by long
exposures, while details in bright areas are
captured by short exposures.
I
To overcome limited dynamic range, we can take
multiple exposures and use image processing to
combine them.
Image Contrast
Definition
The contrast of a grayscale image is the amount to
which different objects in the image can be visually
distinguished from one another.
I
Contrast is how well an image utilizes the range of
pixel intensities available.
I
It is independent of the brightness in an image.
Example: Image Contrast
Low Contrast
Original Contrast
High Contrast
Equation for Contrast?
Unlike brightness, contrast is harder to nail down
mathematically. Many definitions are of the form:
Contrast =
Change in Luminance
Average Luminance
For example, Michelson’s Contrast:
CM (I) =
max(I) − min(I)
max(I) + min(I)
Equation for Contrast?
I
These types of equations make sense for images
with roughly two luminances, i.e., uniform
foreground and background.
I
They do not work well with more complex scenes,
or scenes where max and min pixels occur in small
quantities.
Point Operations
Definition
A point operation on an image is an algorithm that
changes each pixel value according to some function:
I(u, v) 7→ f (I(u, v)).
I
The function f depends only on the pixel value.
I
It is independent of the spatial location (u, v).
I
The domain of f must match the range of I , and the
range of f determines the output image type.
Point Operation Pseudocode
Input: an image I(u, v) defined on [1 . . . w] × [1 . . . h]
Output: new image I 0 (u, v)
for v = 1 . . . h
for u = 1 . . . w
set I 0 (u, v) = f (I(u, v))
Example Point Operation Functions
I
Addition (changes brightness)
f (p) = p + k
I
Multiplication (stretches/shrinks image range)
f (p) = k × p
I
Real-valued functions:
exp(x), log(x), (1/x), xk , etc.
Clamping
The following function will clamp pixel values to fall
within the interval [a, b].


a if p < a
f (p) = p if a ≤ p ≤ b

b if p > b
Intensity Windowing
Definition
Intensity windowing is a clamp operation followed by
linearly stretching the image intensities to fill the full
possible range.
If we want to window an image in [a, b], with max
intensity M :


0
f (p) = M ×

M
p−a
b−a
if p < a
if a ≤ p ≤ b
if p > b
Example: Intensity Windowing
Original Image
Windowed Image
Thresholding
Thresholding converts a grayscale image into a binary
image by making every pixel below some threshold equal
to 0 and every pixel above that threshold equal to 1.
(
0 if p ≤ a
f (p) =
1 if p > a
Example: Thresholding
Original Image
Thresholded Image