Download Computer Vision and Digital Image Processing and more Slides Digital Image Processing in PDF only on Docsity!
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Computer Vision &
Digital Image Processing
Dr. David Jeff Jackson
Electrical & Computer Engineering
The University of Alabama
Elements of visual perception
- Goal: help an observer interpret the content of an
image
- Developing a basic understanding of the visual
process is important
- Brief coverage of human visual perception follows
- Emphasis on concepts that relate to subsequent material
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Cross section of the human eye
- Eye characteristics
- nearly spherical
- approximately 20 mm in diameter
- three membranes
- cornea (transparent) & sclera (opaque) outer cover
- choroid contains a network of blood vessels, heavily pigmented to reduce amount of extraneous light entering the eye. Also contains the iris diaphragm (2-8 mm to allow variable amount of light into the eye)
- retina is the inner most membrane, objects are imaged on the surface
Retinal surface
- Retinal surface is covered in discrete light receptors
- Two classes
- Cones
- 6-7 million located primarily near the center of the retina (the fovea )
- highly sensitive to color
- can resolve fine details because each is attached to a single nerve ending
- Cone vision is called photopic or bright-light vision
- Rods
- 75-150 million distributed over the retinal surface
- multiple rods connected to a single nerve ending
- give a general overall picture of the field of illumination
- not color sensitive but are sensitive to low levels of illumination
- Rod vision is called scotopic or dim-light vision
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Imaging in the eye
- Variable thickness lens: thick for close focus, thin for distant focus
- Distance of focal center of the lens to the retina (14-17 mm)
- Image of a 15m tree at 100m 15/100 = X/17 or approximately 2.55 mm
- Image is almost entirely on the fovea
A simple imaging model
- An image is a 2-D light intensity function f(x,y)
- As light is a form of energy 0 < f(x,y) < ∞
- f(x,y) may be expressed as the product of 2 components f(x,y)=i(x,y)r(x,y)
- i(x,y) is the illumination: 0 < i(x,y) < ∞
- Typical values: 9000 foot-candles sunny day, 100 office room, 0. moonlight
- r(x,y) is the reflectance: 0 < r(x,y) < 1
- r(x,y)=0 implies total absorption
- r(x,y)=1 implies total reflectance
- Typical values: 0.01 black velvet, 0.80 flat white paint, 0.93 snow
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
A simple imaging model (continued)
- The intensity of a monochrome image f at ( x,y ) is the gray level ( l ) of the image at that point
- In practice Lmin =imin r (^) min and Lmax=i (^) maxr (^) max
- As a guideline Lmin ≈ 0.005 and Lmax ≈ 100 for indoor image processing applications
- The interval [Lmin, Lmax] is called the gray scale
- Common practice is to shift the interval to [0,L] where l=0 is considered black and l=L is considered white. All intermediate values are shades of gray
L min (^) ≤ l ≤ L max
Sampling and quantization
- To be suitable for computer processing an image, f(x,y) must be digitized both spatially and in amplitude
- Digitizing the spatial coordinates is called image sampling
- Amplitude digitization is called gray-level quantization
- f(x,y) is approximated by equally spaced samples in the form of an NxM array where each element is a discrete quantity
f N f N f N M
f f f M
f f f M
f x y
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Effects of reducing spatial resolution
Pixel replication occurs as resolution is decreased
256x256 128x
64x64 32x
Effects of reducing gray levels
Ridgelike structures develop as gray level is decreased: false contours
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Basic relationships between pixels
- An image is denoted by: f(x,y)
- Lowercase letters (e.g. p, q ) will denote individual pixels
- A subset of f(x,y) is denoted by S
- Neighbors of a pixel:
- A pixel p at (x,y) has 4 horizontal/vertical neighbors at
- (x+1,y), (x-1,y), (x, y+1) and (x, y-1)
- called the 4-neighbors of p : N 4 (p)
- A pixel p at (x,y) has 4 diagonal neighbors at
- (x+1,y+1), (x+1,y-1), (x-1, y+1) and (x-1, y-1)
- called the diagonal-neighbors of p : ND(p)
- The 4-neighbors and the diagonal-neighbors of p are called the 8-neighbors of p : N 8 (p)
Connectivity between pixels
- Connectivity is an important concept in establishing boundaries of object and components of regions in an image
- When are two pixels connected?
- If they are adjacent in some sense (say they are 4-neighbors)
- and, if their gray levels satisfy a specified criterion of similarity (say they are equal)
- Example: given a binary image (e.g. gray scale = [0,1]), two pixels may be 4-neighbors but are not considered connected unless they have the same value
0 1 1 1
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Pixel adjacencies and paths
- Pixel p is adjacent to q if they are connected
- We can define 4-, 8-, or m-adjacency depending on the specified type of connectivity
- Two image subsets S 1 and S 2 are adjacent if some pixel in S 1 is adjacent to S 2
- A path from p at ( x,y ) to q at ( s,t ) is a sequence of distinct pixels with coordinates (x 0 ,y 0 ), (x 1 ,y 1 ),….., (xn ,yn ) - Where (x 0 ,y 0 )=(x,y) and (xn,yn)=(s,t) and - (xi ,yi ) is adjacent to (x (^) i-1,yi-1 ) for 1<= i <= n - n is the length of the path
- If p and q are in S , then p is connected to q in S if there is a path from p to q consisting entirely of pixels in S
Example paths
A 4-connected path from p to q (n=2). p and q are connected in S 1
An m-connected path from t to q (n=3). t and q are connected in S 2
p
q q
t
Subset S 1 Subset S 2
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Connected components
- For any pixel p in S , the set of pixels connected to p
form a connected component of S
- Distinct connected components in S are said to be
disjoint
3 4-connected components of S
2 m-connected components of S
Labeling 4-connected components
- Consider scanning an image pixel by pixel from left to right and top to bottom - Assume, for the moment, we are interested in 4-connected components - Let p denote the pixel of interest, and r and t denote the upper and left neighbors of p , respectively - The nature of the scanning process assures that r and t have been encountered (and labeled if 1) by the time p is encountered
r
t p
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 2-
Labeling 8-connected components
- Proceed as in the 4-connected component labeling case, but also examine two upper diagonal neighbors ( q and s ) of p
L0 L
L
L
L
L0 L
L
L
L0 L
L
L
L
L0 L
L
L
Before equivalence class labeling
After equivalence class labeling
L1=L
Labeling connected components
in non-binary images
- The 4-connected or 8-connected labeling schemes can be extended to gray level images
- The set V may be used to connect into a component only those pixels within a specified range of pixel values
L
L0 L1 L
L0 L1 L
L
