The document discusses various arithmetic operations that can be performed on images at the pixel level including addition, subtraction, averaging, bitwise operations, and alpha blending. Pseudocode is provided to demonstrate how an operator is applied pairwise to each pixel position in the input images to produce an output image. Examples of applications discussed include double exposures, change detection, motion tracking, video compression, masking, and blue screening.

1. Arithmetic Operations
Image Arithmetic
For input images f1 and f2 and some function Op:
g(x, y) = Op (f1(x, y), f2(x, y))
The operator is applied pairwise to each pixel in the
images.
Pseudocode:
for all pixel positions x, y:
out[x,y] = func( image1[x,y] , image2[x,y]
)
Possibilities: addition, subtraction, and, or, ...

2. Arithmetic Operations
Addition/Blending
Used to create double-exposures or composites:
g(x, y) = f1(x, y) + f2(x, y)
+ =
Can also do a weighted blend:
g(x, y) = α1f1(x, y) + α2f2(x, y)

3. Arithmetic Operations
Subtraction
Useful for finding changes between two images
g(x, y) = f1(x, y) − f2(x, y)
Sometimes more useful to use absolute difference
g(x, y) = |f1(x, y) − f2(x, y)|
What’s changed?
- =

4. Arithmetic Operations
Digital Subtraction Angiography
1. Take an x-ray
2. Inject patient with a radio-opaque dye
(and tell them not to move!)
3. Take another x-ray
4. Subtract the two

5. Arithmetic Operations
Motion
Use differencing to identify motion in an otherwise
unchanging scene (object motion, not camera motion)
Basis for motion tracking techniques in computer vision
Use overall shift (minimum difference) for tracking
camera motion
Part of a larger process called a ”match move” in
film making
Essential for inserting computer-generated graphics into a
real scene with a moving camera
Useful for video compression
Only encode the difference between frames
Motion detection/prediction used extensively in video
compression such as MPEG

6. Arithmetic Operations
Image Averaging
Idea:
Average multiple pictures of the same scene to reduce noise
Similar in principle to acquiring the image for a longer duration.
+ + . . . =

7. Arithmetic Operations
Image Averaging
Top: original image, image with Gaussian additive noise
Middle and Bottom: 8, 16, 64, 128 images averaged

8. Arithmetic Operations
Bitwise AND and OR
Useful for masking

9. Arithmetic Operations
Alpha Blending
Addition of two images, each with (0..1) fractional masking
weights per pixel
g(x, y) = α1(x, y)f1(x, y) + α2(x, y)f2(x, y)
or quite often
g(x, y) = α1(x, y)f1(x, y) + [1 − α1(x, y)]f2(x, y)
Useful for transparency, compositing, etc.
Color images are often stored as RGBα or RGBA

10. Arithmetic Operations
Application: Blue Screening
Goal: composite people/things onto a background
Film against a blue (or green) background
Mask the blue parts
(use fractional alpha values for partial-pixel effect)
“Decontaminate” the blue halo
Store in RBGA format
Composite onto background using alpha blending