1. Digital Image Fundamentals
2.1.3 Bright adaptation and Discrimination
The range of light intensity level to the human system: from the scotopic threshold to glare limit
Brightness adaptation-the total range of distinct intensity level it can discriminate is small when compared with the total adaptation range
Subjective brightness: is a logarithmic function of the light intensity incident on the eye
Brightness adaptation level: the current sensitivity level of the visual system (Ba)
The range of subjective brightness that the eye can perceive when adapted to this level (Bb)
A level at and below (Bb)-indistinguishable black

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3. Experiment of Weber Ratio
Chapter 2: Digital Image Fundamentals
Experiment of Weber Ratio
Good brightness discrimination

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Mach band: a brightness pattern that is strongly scalloped, especially near the boundary (Fig. 2.7(b))
Simultaneous contrast: a region’s perceived brightness does not simply depend on its intensity (Fig. 2.8)

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Optical illusion—eye fills in nonexisting information or wrongly perceive geometrical properties of objects

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12. 2.3 Image sensing and acquisition
Acquisition using a single sensor
Microdensitometer
A laser source coincident with the sensor
Acquisition using a sensor strips
Imaging acquisition using in-line sensors
Computerized axial tomography
Imaging acquisition using array sensors
Electromagnetic and ultrasonic sensing devices
CCD sensors - charge-coupled device
A simple image formation model
2-D Image function : f(x,y)
May be characterized by : amount of source illumination incident on the scene and amount of illumination reflected by the objects: f(x,y)= I(x,y) r(x,y)

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16. 2.4 Image sampling and quantization
Convert the continuous sensed data to digital form
Sampling
Spatial transform: spatial coordinates(discrete locations)
Quantization
Amplitude transform: gray levels are converted to discrete values
The quality of a digital image
is determined to a large degree
by the number of samples and
discrete gray levels

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18. 2.4.2 Representing digital images
The complete MN digital image in the matrix form: f(x,y)
Pixel, picture element
A digital image use a traditional matrix A
The number of gray levels L= 2k
The dynamic range of an image : the range of values spanned by the gray scale
High contrast image : an image whose gray levels span a significant portion of the gray scale as having a high dynamic range
The number, b, of bits required to store a digitized image is
b=M N K

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20. 2.4.3 Spatial and gray-level resolution
Sampling is the principal factor determining the spatial resolution
Gray-level resolution: the smallest قابل للإدراك discernible range in gray level
is the power of 2 due to hardware considerations
The most common number: 8 bits
Spatial resolution
Sub-sampling
Resampling
Keep the number of samples constant and reduce the number of gray levels
Reduce the number of bits while keeping the spatial constant
Vary N and k simultaneously
ISO reference curves
If the number of bit are fixed, how to adjust the trade-off between spatial and gray-level resolution?

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27. 2.4.4 Aliasing and Moire patterns
frequency spectrum in terms of sines /cosines of various frequencies
Band-limited functions
the highest frequency is finite and that the function is of unlimited duration
The Shannon sampling theorem
if the function is sampled at a rate equal to or greater than twice its samples
Under-sampled
aliasing corrupts the sampled image
Additional frequency component are introduced into the sampled function (aliased frequencies)
Sampling rate is the number of samples taken per unit distance
It is impossible to satisfy the sampling theorem
Sol: work with sampled data that are finite in duration
Gating function: convert a function of unlimited duration into a function of finite duration by multiplying a “ gating function”

28. Reducing the aliasing effect : reduce its high frequency by blurring the image
Moirie patterns: a function of finite duration can be sampled over a finite interval without violating the sampling theorem
Moirie patterns caused by a break up of the periodicity caused by interference between two sets of fine pattern grids, the scanner samples and the halftone screen in the original image

31. 2.4.5 zooming and shrinking digital images
Two steps for zooming
(1) the creation of new pixel locations
(2) the assignment of gray levels to those new locations
neighbor interpolation الزيادة : nearest neighborhood interpolation
Pixel replication الإستنساخ
Increase the size of an image an integer number of times
a special case of nearest neighbor interpolation (Figs. 2.20(b)
Defect: produces a checkerboard effect
Bilinear interpolation
Image shrinking
Equivalent process of pixel location is row-column deletion:shrink by a non-integer factor
Expand the grid to fit over the original image
Do gray-level nearest neighbor or bilinear interpolation
Shrink the grid to its original specified size
Defect: Aliasing effect
Sol: blur an image slightly

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33. 2.5 Some basic relationship between pixels 2.5.1 Neighbor of a pixel
Horizontal and vertical neighbors
4-neighbors of p
8-neighbors of p
Four diagonal neighbors
2.5.2 Adjacency, connectivity, regions, and boundaries
Connectivity of two pixels: if two pixels are connected, it must be determined
If they are neighbors
If their gray levels satisfy a specified criterion of similarity
Three types of adjacency: 4-adjacency N4(V), 8-adjacency N8(V), m-adjacency(mixed adjacency)
Digital path or curve
Closed path
4-, 8-, or m-paths

35. Two pixels are said to be connected in S Boundary
Connected component of S
Connected set
Boundary
A region of the image R: R is a connected set
The boundary of a region R: the set of pixels in the region that have one or more neighbors
Edge
2.5.3 Distant measures
Distant function or metric
The Eulidean distance between p and q
D4 (city block) distance :
D8 (chessboard block) distance
Dm distance: the shortest m-path between the points
2.5.4 Image operation on a pixel basis
Operation is carried out between corresponding pixels
2.6 linear and nonlinear operations
H(af+bg)= aH(f) + b H(g)

36. Euclidean distance
De(p, q) = [(x - s)2 + (y - t)2 ]1/2
TheD4 distance (also called city-block distance) between p and q is defined as
D4(p, q) = |x – s| + |y – t|
TheD8 distance (also called chessboard distance) between p and q is defined as
D8(p, q) = max (|x – s|, |y – t|)

38. (a) When V = {0, 1}, 4 path does not exist between p and q because it is impossible to get from p to q by traveling along points that are both 4adjacent and also have values from V . Figure P2.15(a) shows this condition it is not possible to get to q.
The shortest 8path is shown in Fig. P2.15(b) its length is 4. In this case the length of shortest m- and 8paths is the same. Both of these shortest paths are unique in this case.
(b) One possibility for the shortest 4path when V = (1, 2) is shown in Fig. P2.15(c) its length is 6. It is easily verified that another 4path of the same length exists between p and q.
One possibility for the shortest 8path (it is not unique) is shown in Fig. P2.15(d) its length is 4. The length of a shortest mpath
similarly is 4.