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Digital Image Processing, 2nd ed.www.imageprocessingbook.com
2002 R. C. Gonzalez & R. E. Woods
Chapter 2: Digital Image Fundamentals
-Cornea(Gic mc)
- Sclera (Mng cng)
- Iris(Mng mt)
- Lens(Thu knh)
- Retina(Vng mc)
- Visual Axis
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2002 R. C. Gonzalez & R. E. Woods
Chapter 2: Digital Image Fundamentals
- Cones: 6~7 millions are distributed around fovea. Highly sensitive to
color. Human resolve fine details with these.
- Rods: 75~150 millions are distributed over the retinal surface.
Several rods are connected to a single nerve end. Reduce the amount of
detail. Serve to give a general, overall picture of the field of view.
Sensitive to low levels of illumination.
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2002 R. C. Gonzalez & R. E. Woods
Chapter 2: Digital Image Fundamentals
-Shape of the lens is controlled by the controlling muscles
- The muscles make the lens to be relatively flattened for
distant objects.
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2002 R. C. Gonzalez & R. E. Woods
Brightness Adaptation
The total range of intensity levels
that it can discriminate
simultaneously is rather small
compared with the total adaptation
range
Ba
is a brightness adaptation
level The short intersecting curve
represents the range of subjective
brightness that the eye can
perceive when adapted to this
level.
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2002 R. C. Gonzalez & R. E. Woods
Contrast Sensitivity
The ability of the eye to
discrimination between changes
in brightness at specific
adaptation level
I is uniform illumination on
a flat background area large
enough to occupy the entire
field of view
is the change in the
object brightness required to
just distinguish the object
from the background
Weber ratio: I/I
- Bad brightness discrimination
if Weber Ratio is large,
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2002 R. C. Gonzalez & R. E. Woods
Weber Ratio
Brightness discrimination is
poor (the Weber ratio is large) at
low levels of illumination and
improves significantly (the ratiodecreases) as background
illumination increases.
hard to distinguish the
discrimination when it is brightarea but easier when the
discrimination is on a dark area.
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2002 R. C. Gonzalez & R. E. Woods
Brightness vs. Function of intensity
Visual system tends toundershoot or overshoot around
the boundary of regions of
different intensities.
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2002 R. C. Gonzalez & R. E. Woods
Simultaneous Contrast
All the small squares have exactly the same intensity, butthey appear to the eye progressively darker as the background
becomes brighter.
Regions perceived brightness does not depend simply onits intensity.
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Optical Illusions
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Electromagnetic Spectrum
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2002 R. C. Gonzalez & R. E. Woods
Signal
A signal is a function that carries information.
Usually content of the signal changes over some set of
spatiotemporal dimensions.Time-Varying Signal: f(t)
Ex) audio signal
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2002 R. C. Gonzalez & R. E. Woods
Spatially-Varying Signal
Signals can vary over space as well.
An image can be thought of as being a function of 2
spatial dimensions:
f(x,y)for monochromatic images, the value of the function is the
amount of light at that point.
medical CAT and MRI scanners produce images that are
functions of 3 spatial dimensions:
f(x,y,z)
Spatiotemporal Signals:
f(x,y,t)
ex) a video signal, animation
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2002 R. C. Gonzalez & R. E. Woods
Analog and Digital Signal
Most naturally-occurring signals also have a real-
valued range in which values occur with infinite
precision.To store and manipulate signals by computer we
need to store these numbers with finite precision.
thus, these signals have a discrete range.
signal has continuous domain and range = analog
signal has discrete domain and range = digital
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Sampling
sampling = the spacing of discrete values in the domain ofa signal.
sampling-rate = how many samples are taken per unit ofeach dimension. e.g.,samples per second, frames per second
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2002 R. C. Gonzalez & R. E. Woods
Quantization
Quantization = spacing of discrete values in therange of a signal.
Usually thought of as the number of bits persample of the signal.
e.g., 1, 8, 24 bit images, 16-bit audio.
l d d
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2002 R. C. Gonzalez & R. E. Woods
Digital Image Representation
A digital image is an image f(x,y)
that has been digitized both in spatialcoordinates and brightness.
The value of f at any point (x,y) is
proportional to the brightness (or
gray level) of the image at that point.
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2D Image Sensor
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Coordinate Conversion used in this book
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Digital Image Acquisition Process
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Sampling and Quantization
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Example of Digital Image
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Sampling Effect
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Sampling Effect
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Sampling Effect
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Quantization Effect
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2002 R. C. Gonzalez & R. E. Woods
Quantization Effect
if the gray scale is not
enough, the smooth area willbe affected.
False contouring can occur
on the smooth area which has
fine gray scales.
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Light-intensity function
image refers to a 2D light-intensityfunction, f(x,y)
the amplitude of f at spatial coordinates
(x,y) gives the intensity (brightness) of the
image at that point.
light is a form of energy thus f(x,y) mustbe nonzero and finite.
0 < f(x,y)<
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2002 R. C. Gonzalez & R. E. Woods
Illumination and Reflectance
The basic nature of f(x,y) may becharacterized by 2 components:
the amount of source light incident
on the scene being viewed
Illumination, i(x,y)
the amount of light reflected by the
objects in the scene
Reflectance, r(x,y)
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2002 R. C. Gonzalez & R. E. Woods
Illumination and Reflectance
f(x,y) = i(x,y)r(x,y)
i(x,y):
determined by the nature of the light sourcebounded by
0 < i(x,y)<
r(x,y) :
determined by the nature of the objectsbounded by
0 < r(x,y)< 1
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2002 R. C. Gonzalez & R. E. Woods
Gray Level
we call the intensity of a monochrome image f at
coordinate (x,y) the gray level (l) of the image at
that point.thus, l lies in the range Lmin l Lmax
Lminand Lmaxare positive and finite.
gray scale = [Lmin, Lmax]
common practice, shift the interval to [0, L ]0 = black , L = white
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Resolution
Resolution (how much you can see the detail of
the image) depends on sampling and gray levels.
the bigger the sampling rate (n) and the gray scale(g), the better the approximation of the digitized
image from the original. But the size of the image
gets bigger
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Non-uniform Sampling
For a fixed value of spatial resolution, the
appearance of the image can be improved by
using adaptive sampling rates.Fine sampling
Required in the neighborhood of sharp
gray-level transitions.Coarse sampling
Utilized in relatively smooth regions.
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Chapter 2: Digital Image Fundamentals
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Chapter 2: Digital Image Fundamentals
For the images with a
large amount of detail
only a few gray levelsmay be needed.
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2002 R. C. Gonzalez & R. E. Woods
Non-uniform Quantization
unequally spaced levels in quantization process
influences on the decreasing the number of gray
level.use few gray levels in the neighborhood of
boundaries.
use more gray levels on smooth area in order to
avoid the false contouring.
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2002 R. C. Gonzalez & R. E. Woods
Basic Relationship amongpixels
Neighbors of a pixelConnectivity
Labeling of Connected ComponentsDistance Measures
Arithmetic/Logic Operations
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Neighbors of a Pixels
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Connectivity
Let V be the set of gray-level values used to defined connectivity4-connectivity :
2 pixels p and q with values from V are 4-connected if q is in the
set N4(p)
8-connectivity :
2 pixels p and q with values from V are 8-connected if q is in the set
N8(p)
m-connectivity (mixed connectivity):
2 pixels p and q with values from V are m-connected if
q is in the set N4(p) orq is in the set ND(p) and the set N4(p)N4(q) is empty.(the set of pixels that are 4-neighbors of both p and q whose
values are from V )
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Example of Connectivity
Path 8 neighbors m neighbors
m-connectivity eliminates the multiple pathconnections that arise in 8-connectivity.
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Path
a path from pixel p with coordinates (x,y) to pixel
q with coordinates (s,t) is a sequence of distinct
pixels with coordinates(x0,y0),(x1,y1),(xn,yn)
, where (x0,y0) = (x,y) , (xn,yn) = (s,t) and (xi,yi) is
adjacent to (xi-1,yi-1)
n is the length of the pathwe can define 4-,8-, or m-paths depending on
type of adjacency specified.
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Adjacent
A pixel p is adjacent to a pixel q if they are
connected.
Two image area subsets S1 and S2 areadjacent if some pixel in S1 is adjacent to
some pixel S2.
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Labeling 1
Scan the image from left to right
Let p denote the pixel at any step in the scanning
process.
Let r denote the upper neighbor of p.Let t denote the left-hand neighbors of p,
respectively.
When we get to p, points r and t have already
been encountered and labeled if they were 1s.r
t p
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Labeling 2
if the value of p = 0, move on.
if the value of p = 1, examine r and t.
if they are both 0, assign a new label to p.
if only one of them is 1, assign its label to p.if they are both 1
if they have the same label, assign that label to p.
if not, assign one of the labels to p and make a note that
the two labels are equivalent. (r and t are connected
through p).At the end of the scan, all points with value 1 have been
labeled.
Do a second scan, assign a new label for each equivalent
labels.
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Labeling with 8 connected components
do the same way but examine also the upper
diagonal neighbors of p.
if p is 0, move on.
if p is 1
if all four neighbors are 0, assign a new label to p.if only one of the neighbors is 1, assign its label to p.
if two or more neighbors are 1, assign one of the
label to p and make a note of equivalent classes.
after complete the scan, do the second round and
introduce a unique label to each equivalent class.
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Distance Measures
for pixel p, q and z with coordinates (x,y),
(s,t) and (u,v) respectively,
D is a distance function or metric if
(a) D(p,q) 0 ; D(p,q) = 0 iff p=q
(b) D(p,q) = D(q,p)(c) D(p,z) D(p,q) + D(q,z)
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Euclidean Distance
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g p g
2002 R. C. Gonzalez & R. E. Woods
City-Block Distance
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g p g
2002 R. C. Gonzalez & R. E. Woods
Chessboard Distance
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g p g
2002 R. C. Gonzalez & R. E. Woods
M-connectivity distances
distances of m-connectivity of the pathbetween 2 pixels depends on values of pixelsalong the path.
e.g., if only connectivity of pixels valued 1 isallowed. find the m-distance between p and p4
p3 p4 0 1 1 1 1 1
p1 p2 0 1 0 1 1 1
p 1 1 1
d = 2 d=3 d=4
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Linear and Nonlinear Operations
An operator H is said to be alinearoperatorif it satisfy the following conditions.
H(af - bg) = aH(f) + bH(g)
where f and g are images and a and b are scalarsThe sum of two images is identical to applyingthe operator to the image individually, muliplyingthe results by the constants, and adding those
results.An operator that fails the test of aboveequation is nonlinear. Ex) |afbg|