What is Digital Image Processing?

1
What is Digital Image Processing?

• An image is defined as a two-dimensional
  function, f(x,y), where x and y are spatial
  (plane) coordinates, and the amplitude of f at
  any pair of coordinates (x,y) is called the
  intensity of the image at that point.
• When x, y and the amplitude of f are all finite,
  discrete quantities, we call the image a digital
  image.
• The field of digital image processing refers to
  processing digital images by using computers.
• A digital image consists of a finite number of
  elements, each of which has a particular location
  and value.
• The elements are referred as picture elements,
  image elements, pels and pixels.

2
Machines vs humans

• Among the five senses, vision is considered to be
  vital one for a human being.
• But a human being can perceive only visible part
  of the electromagnetic spectrum.
• But machines can span the entire range of
  electromagnetic spectrum from gamma to radio
  waves.

3
Image vision vs Image analysis

• Image processing is a branch in which both the
  input and output of a process are images.
• The goal of computer vision is to use computers
  to emulate human vision, including learning,
  making inferences and taking actions.
• The area of image analysis is in between image
  processing and computer vision.

4
Types of Processes in Image Processing

• There are 3 types of computerized processes.
• They are low, mid and high level processes.
• Low-level processes involve primitive operations
  such as image preprocessing to reduce noise,
  contrast enhancement and image sharpening.
• Here both the input and output are images.
• Mid-level processing involves segmentation
  (partitioning image into regions), description of
  objects to reduce them to a form so that a
  computer can process and classification
  (recognition) of objects.
• Here inputs are images but outputs are attributes
  extracted from images.
• In high-level processing, we make sense of a
  collection of recognized objects.

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Example of dip and image analysis

• The process of acquiring an image of a text,
  processing it, extracting (segmenting) individual
  characters, describing characters suitable for
  computer processing and recognizing those
  individual characters are in the scope of digital
  image processing.
• Making sense of the content of the page (text) is
  viewed as the domain of image analysis and
  computer vision.

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Categorizing Images

• One can categorize images according to their
  source.
• One of the main sources is due to electromagnetic
  spectrum.
• The electromagnetic spectrum arranged according
  to energy per photon
• The spectra band ranges from gamma rays (high
  energy), X-rays, Ultraviolet, Visible, Infrared,
  Microwaves to radio waves (low energy).
• Other sources are acoustic, ultrasonic and
  electronic (electron beams used in electron
  microscopy).

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Gamma Ray Imaging

• These are used in nuclear medicine and
  astronomical observations.
• In medicine, it is used for complete bone scan.
• The nuclear imaging is also used in positron
  emission tomography (PET).
• It can render the 3-D image of patients.
• It can detect tumors in the brain and lungs.
• The images of stars which exploded about 15000
  years ago, can be captured using gamma rays.

8
Examples of Gamma Ray Images(Bone scan and PET
images)
9
X-ray Imaging

• It is also used in medicine and astronomy.
• We can get images of blood vessels in
  angiography.
• It is also used in Computerized Axial Tomography
  (CAT) to generate 3-D rendition of a patient.
• High energy X-ray images are used in industrial
  processes (electronic circuit board).

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Examples of X-ray Images(Chest X-ray and Circuit
boards)
11
Ultraviolet Imaging

• It is used in lithography, industrial inspection,
  microscopy, lasers, biological imaging and
  astronomical observations.
• Corn, cereals, onions caused by parasitic fungi
  can be identified using this imaging technique.

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Examples of Ultraviolet Images(Normal corn vs
Smut corn)
13
Visible and Infrared Images

• It is used in light microscopy, astronomy, remote
  sensing, industry and law enforcement.
• It is mainly used in weather observation and
  prediction.
• Visual inspection of manufactured goods use
  visible spectrum.
• Automated counting, license plate reading,
  tracking and identifying bills, etc belong to
  visible images.
• Infrared images are used for night vision systems.

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Examples of visible and infrared images
(Microprocessor and surface of an audio CD)
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Microwave Images (Thumb print and paper currency)
Radar images belong to this category. It can
penetrate the inaccessible regions of earths
surface.
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Radio Images(MRI of human knee and spine)
It is used in Magnetic Resonance Imaging (MRI).
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Acoustic imaging

• The images use sound energy.
• They are used in geological exploration, industry
  and medicine.
• It is also used in mineral and oil exploration.
• Ultrasonic images are used in obstetrics to
  determine the health of unborn babies and
  determining the sex of the baby.

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Cross-sectional image of a seismic model
The arrow points to a hydrocarbon (oil and/or
gas) trap.
19
Fundamental steps in Digital Image Processing
20
Fundamental steps of DIP

• Image acquisition This stage involves
  preprocessing, such as scaling.
• Image enhancement Here we bring out details
  that were obscured or highlight some features of
  interest in an image. (eg) increasing the
  contrast of an image.
• Image Restoration Here we talk about how to
  improve the appearance of an image. Unlike
  enhancement, which is subjective, this is
  objective.
• Color Image Processing Due to Internet, this
  area is becoming popular. Various color models
  are worthy to know.
• Wavelets Representing the images in various
  degrees of resolution in the basis of wavelets.

21
Fundamental steps of DIP

• Compression It is a technique for reducing the
  storage required to save an image or bandwidth
  needed to transmit.
• Morphological Processing It deals with tools
  for extracting image components that are useful
  in the representation and description of shape.
• Segmentation These procedures partition an
  image into its constituent parts or objects.
• Representation and description It follows the
  output of a segmentation stage.
• It uses either the boundary of a region or all
  the points in the region itself.
• Description ( also called feature selection)
  deals with extracting attributes or are basic for
  differentiating one class of objects from
  another.
• Recognition It is the process that assigns a
  label (eg. Vehicle) to an object based on its
  descriptors.

22
Components of an Image Processing System
23
Basic components of a general-purpose system used
for digital image processing

• Image sensors Two elements are needed to
  acquire digital images.
• First one is the physical device that is
  sensitive to energy radiated by the object that
  we want to image.
• The second one, called the digitizer, is a device
  for converting the output of the physical sensing
  device into digital form.
• (eg) in a digital video camera, the sensors
  produce an electrical output proportional to
  light intensity.
• The digitizer converts these outputs to digital
  data.

24
Basic components of a general-purpose system used
for digital image processing

• Specialized Image Processing Hardware -
• It consists of digitizer plus hardware that
  performs other primitive operations such as an
  arithmetic logic unit (ALU), which performs
  arithmetic and logical operations on entire
  image.
• This type of hardware is also called as front-end
  subsystem and its characteristic is speed.
• This unit does things that require fast data
  throughputs which main computer cannot handle.
• Computer In an image processing system it is a
  general-purpose computer.
• Software It consists of specialized modules
  that does specific tasks (eg. matlab)

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Basic components of a general-purpose system used
for digital image processing

• Mass storage An image of 1024 X 1024 size,
  storing the intensity of each pixel in 8 bits,
  requires one megabyte of storage.
• For short-time storage, we can use computer
  memory.
• Another method is to use a specialized board
  called frame buffer, that store one or more
  images and can be accessed rapidly.
• They enable us to instantaneously zoom, scroll
  (vertical shift) and pan (horizontal shift).
• For on-line storage magnetic disks or
  optical-media are used.
• The archival storage needs massive capacity but
  are accessed infrequently.
• Image Displays These are mainly color TV
  monitors.
• Hardcopy These devices include laser printers,
  film cameras, inkjet units, etc.

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Brightness Adaptation

• There are 2 phenomena which clearly demonstrate
  that the perceived brightness is not a simple
  function of intensity.
• The visual system tends to undershoot or
  overshoot around the boundary of regions of
  different intensities.
• These scalloped bands near the boundaries are
  called Mach bands.

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creating mach band clear all close all
clc for i1256 for j1256 if j
gt224 f(i,j) 224 elseif j
gt192 f(i,j)192 elseif j gt
160 f(i,j)160 elseif j
gt128 f(i,j)128 elseif
jgt96 f(i,j)96 elseif jgt64
f(i,j)64 elseif jgt32
f(i,j)32 else
f(i,j)5 end
end end f uint8(f) figure,imshow(f) v
f(1,1256) figure,plot(v)
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Simultaneous Contrast

• The simultaneous contrast means a regions
  perceived brightness does not depend simply on
  its intensity.
• For example, all centre squares have exactly same
  intensity.
• But they appear to the eye to become darker as
  the background gets lighter.

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Simultaneous Contrast
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simultanious contrast create a small
Square(gray valued) inside a larger(black)
Square change the intensity of black square and
observe the contrast variation clear all close
all clc for i1256 for j1256 if
(igt64jgt64)(ilt192jlt192)
f(i,j)64 else f(i,j)200
end end end f uint8(f) figure,imshow
(f),title('Fig 1') for i1256 for j1256
if (igt64jgt64)(ilt192jlt192)
f1(i,j)64 else
f1(i,j)128 end end end f1
uint8(f1) figure,imshow(f1),title('Fig 2') for
i1256 for j1256 if
(igt64jgt64)(ilt192jlt192)
f2(i,j)64 else f2(i,j)5
end end end f2 uint8(f2) figure,imsh
ow(f2),title('Fig 3') subplot(1,3,1),imshow(f2)
subplot(1,3,2),imshow(f1) subplot(1,3,3),imshow(f
)
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Chess Board
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Chess board creation

• clear all close all clc
• f checkerboard(8)
• f imresize(f,256,256)
• imshow(f)

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Exercises

• Write a matlab code to create the Mach bands and
  observe the transition of intensities for various
  pixel positions in the Mach band.
• Write a matlab code to simulate simultanious
  contrast - create a small Square(gray valued)
  inside a larger(black) square - change the
  intensity of black square and observe the
  contrast variation.
• Write a matlab code to generate a chessboard
  consisting of eight alternating black and white
  squares.
• Write a matlab code to generate the 1D barcodes
  (EAN-13) that are used in ISBN.
• Write a matlab code to generate the 2D barcodes.
• Write a matlab code to generate the visual code
  for the given ID (83 bits)

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EAN-13 Barcode(European Article Numbering)
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Anatomy of a Visual Code

• A larger and a smaller guide bar for determining
  the location and orientation of the code
• Three cornerstones for detecting the distortion
• The data area with the actual code bits.

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Anatomy of a Visual Code

• The code can be considered as a matrix grid of 11
  x 11 dimensions.
• Each of the blackened cell represents binary 1
  and unblackened cell represents binary 0.
• Thus grid contains 83 bits that can be encoded.
• 3 cells are occupied by the 3 cornerstones, 5
  cells by the horizontal guide bar and 7 cells by
  the vertical guide bar.
• Three cells surrounding each of the three
  cornerstones and fourteen cells surrounding both
  the major and the minor guide are left blank in
  order to recognize them properly.
• Thus out of the 121 bits only 83 bits are used
  for encoding purpose.

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Image Formation Model
39
Image Formation Model

• When an image is generated from a physical
  process, its values are proportional to energy
  radiated by a physical source (em waves).
• Hence f(x,y) must be nonzero and finite. That is
  
• The function f(x,y) is characterized by 2
  components.
• 1) The amount of source illumination incident on
  the scene being viewed called illumination
  component denoted as i(x,y)
• 2) The amount of illumination reflected by the
  objects in the scene called reflectance component
  denoted as r(x,y).

40
Image Formation Model

• where
• and
• When r(x,y) is zero, we have total absorption and
  when it is 1, we have total reflectance.
• The nature of i(x,y) is determined by the
  illumination source and r(x,y) is determined by
  the characteristics of the imaged objects.
• If the images are formed via transmission of
  illumination through a medium such as a chest
  X-ray, we use transmissivity instead of
  reflectivity function.

41
Illumination values of objects

• On a clear day, sun produces about 90000 lm/m2 of
  illumination on the surface of the Earth. It is
  about 10000 lm/ m2 on a cloudy day.
• On a clear evening, a full moon gives about 0.1
  lm/ m2 of illumination.
• The typical illumination of an office is about
  1000 lm/m2.
• The typical values of r(x,y) are 0.01 for black
  velvet, 0.65 for stainless steel, 0.8 for white
  wall paint, 0.90 for silver plated metal and 0.93
  for snow.

42
Image Sampling

• The output of many sensors is continuous voltage.
  
• To get a digital image, we need to convert this
  voltage into digital form.
• But this involves 2 processes, namely sampling
  and quantization.
• An image is continuous with respect to x and y
  coordinates and in amplitude.
• Digitizing the coordinates is called sampling.
• Digitizing the amplitude is called quantization.

43
Sampling and Quantization

• Let us consider a gray scale image.
• We can take intensity values along a particular
  line.
• Subsequently, we consider few equally spaced
  points (discrete locations) along this line and
  mark the intensity values at these points called
  sampling points.
• But the values of amplitude are continuous in
  nature.
• The gray level values can also be converted
  (quantized) into discrete quantities.
• This is called quantization.
• We have converted the gray level ranges into 4
  levels.
• For this we assign one of the 4 discrete gray
  levels (closest one) to each sample.

44
Image to be sampled and quantized along a scan
line
45
The intensity variation sampled at regular
intervals along the scan line
46
Four level intensity quantization of sampled scan
line
47
Code for sampling quantization

• sampling Quantization
• Read a gray scale image and find the amplitude
  along a scan line.
• Sample the scan line amplitude for various
  sampling intervels and plot it
• Quantize the sampled scaned line for various
  Quantization levels.
• f imread('westconcordorthophoto.png')
• mi min(min(f))
• ma max(max(f))
• m n size(f)
• v f(50,1n)
• x(1256) 1256
• s input('give sampling interval (multiples of
  2) ')
• v1 f(50,1sn)
• l input('give quantization levels(multiples of
  2)')
• for i1size(v1,2)
• v2(i) round(v1(i)/(256/l))(256/l)
• end
• figure,plot(v2,'.')

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Representing a Digital Image
49
Representing an image as a Matrix

• The result of sampling and quantization is a
  matrix of real numbers.
• Thus a sampled digital image has M rows and N
  columns.
• The values of the coordinates (x,y) also has
  become discrete due to quantization.
• Thus we can write a M X N digital image as
• f(0,0) f(0,1) f(0,N-1)
• f(1,0) f(1,1) f(1,N-1)
• f(x,y) . . .
• f(M-1,0) f(M-1,1) f(M-1,N-1)

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Dynamic range of an image

• The range of values spanned by the gray scale is
  called dynamic range of an image.
• An image with high dynamic range is said to be a
  high contrast image.
• An image with low dynamic range leads to a dull,
  washed out look.
• The number of bits required to store a digitized
  image is
• When M N, b Nk
• For example, a 256 X 256 image represented with 8
  bits takes 5,24,288 bits.

51
Dynamic Range of Images
52
Spatial and Gray-Level Resolution

• Sampling determines the spatial resolution of an
  image.
• Resolution is the smallest number of discernible
  line pairs per unit distance.
• Gray-level resolution is the smallest discernible
  change in gray level.

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Image to be sub sampled
54
Sub sampled images
55
Subsampling

• The subsampling is achieved by deleting
  appropriate number of rows and columns from the
  original image.
• For example, we can get a 256 X 256 image by
  deleting the every other row and column from the
  512 X 512 image.
• In order to see the effect of subsampling, we can
  replicate appropriate rows and columns of 256 X
  256 to bring it to 512 X 512 size.
• We notice the checkboard pattern.

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Code for checkboard effect

• sampling Quantization
• Read a gray scale image and find the amplitude
  along a scan line.
• Sample the scan line amplitude for various
  sampling intervels and plot it
• Quantize the sampled scaned line for various
  Quantization levels.
• clear all close all clc
• f imread('westconcordorthophoto.png')
• m n size(f)
• v f(50,1n)
• x(1256) 1256
• figure,imshow(f),title('Original Image')
• s input('give sampling interval (multiples of
  2) ')
• v1 f(1sm,1sn)
• figure,imshow(v1),title('Sampled Image')
• l input('give quantization levels(multiples of
  2)')
• for i1m
• for j1n
• v2(i,j) round(v1(i,j)/(256/l))(256/l)
• end
• end

58
False contouring

• We can keep the number of samples constant and
  reduce the number of gay levels also from 256 to
  128, 64, etc.
• This creates imperceptible set of very fine
  ridgelike structures in areas of smooth gray
  levels, called false contouring.
• It is prominent in an image which is displayed
  with 16 or less gray levels.

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Isopreference curve (Assignment)

• Let us collect 3 different digital images of same
  size but taken at different locations and
  lighting conditions.
• Gradually reduce the size N and gray levels k.
• Ask an observer to rank the images according to
  their subjective quality.
• Plot the curve in the Nk plane.
• This is called isopreference curve.
• A shift up and right in the curves means it is a
  better picture.

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Isopreference curve
62
Zooming and Shrinking Digital Images

• Zooming is viewed as oversampling and shrinking
  is viewed as under sampling.
• Zooming is a 2 step process the creation of new
  pixel locations and assignment of gray levels to
  those new locations.
• For example, say we want to zoom an image of size
  500 X 500 to 750 X 750.
• We can use nearest neighbor interpolation for
  zooming.
• Pixel replication is the special case of nearest
  neighbor interpolation.
• Pixel replication is used to zoom the image by an
  integer number of times.
• Here new locations are exact duplicates of old
  locations.
• It is very fast but produces check board effect
  and hence is undesirable for larger magnification.

63
Bilinear interpolation

• The best way is to use bilinear interpolation
  using four nearest neighbors of a point.
• Let (x,y) denote the coordinates of a point in
  the zoomed image and let v(x,y) denote the gray
  level assigned to it.
• The assigned gray level is given by
• v(x,y) ax by cxy d
• Here the four coefficients are determined from
  the 4 equations in four unknowns that can be
  written using the 4 nearest neighbors of point
  (x,y). (Assignment)

64
Shrinking an image

• For shrinking an image by one-half, we delete
  every other row and column.
• In order to shrink an image by non integer
  factor, we expand the grid to fit over the
  original image, do gray-level nearest neighbor or
  bilinear interpolation, and then shrink the grid
  back to its original specified size.
  (Assignment).
• It is good to blur an image slightly before
  shrinking it.

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Image zooming using nearest neighbor gray-level
interpolation
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Image Zooming using bilinear interpolation
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Read a sub-sampled image. Using column and row
replicative technique magnify the image to an
appropriate size. clear all close all
clc aimread('cameraman.tif') aim2double(a) m
nsize(a) sp input('enter how many times the
image to be doubled') ssp1 disp('your image
will be magnified by ',num2str(power(2,sp)),'times
') figure,imshow(a) m12m n12n
I1 J1 for i12m1 for j12n1
b(i,j)a(I,J) JJ1
end II1 J1 end
for i22m1 for j22n1
b(i,j)b(i-1,j-1) end
end for i12m1 for j22n1
b(i,j)b(i,j-1) end
end for i22m1 for j12n1
b(i,j)b(i-1,j) end
end figure,imshow(b)
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Relationships between PixelsNeighbors of a Pixel

• A pixel p at coordinates (x,y) has 4 horizontal
  and vertical neighbors whose coordinates are
  given by
• (x1,y), (x-1,y), (x,y1), (x,y-1).
• This set of pixels is called the 4-neighbors of p
  and is denoted by N4(p). Some of the neighbors
  of p lie outside the image if (x,y) is on the
  border of the image.
• The four diagonal neighbors of p have coordinates
• (x1, y1), (x1, y-1), (x-1, y1), (x-1, y-1)
• And are denoted by ND(p). These points, along
  with 4-neighbors are called 8-neighbors of p,
  denoted by N8(p).

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Adjacency and Connectivity

• To establish if 2 pixels are connected, it must
  be determined if they are neighbors and if their
  gray levels satisfy a specified criterion of
  similarity.
• (eg) in a binary image, 2 pixels may be 4
  neighbors but they are said to be connected only
  if they have the same value.
• In a gray scale image, we consider any subset of
  allowed gray level values for connectivity.

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3 types of adjacency

• 4-adjacency Two pixels p and q with values from
  V are 4 adjacent if q is in the set N4(q).
• 8-adjacenty Two pixels p and q with values from
  V are 8-adjacent if q is in the set N8(q).
• m-adjacency Two pixels p and q with values from
  V are m-adjacent if
• q is in N4(p), or
• q is in ND(p) and set N4(p) n N4(q) has no pixels
  whose values are from V.

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Digital Path
Arrangement of pixels pixels that
are 8-adjacecnt (dashed)
A (digital) path (or curve) 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
) Here n is the length of the path. If (x0 ,
y0) (xn , yn ), the path is a closed path.
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Distance Measures

• For pixels p, q and z with coordinates (x,y),
  (s,t) and (v,w) respectively, D is a distance
  function or metric if
• D(p,q) 0 (D(p,q) 0 iff p q)
• D(p,q) D(q,p) and
• D(p,z) D(p,q) D(q,z)
• The Euclidean distance between p and q is defined
  as
• De(p,q) (x s)2 (y t)21/2
• Here the pixels having a distance less than or
  equal to some value r from (x,y) are the points
  contained in a disk of radius r centered at (x,y)

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D4 distance

• The D4 distance (called city-block distance)
  between p and q is defined as
• D4(p,q) x s y t.
• Here the pixels have a D4 distance from (x,y)
  less than or equal to some value r form a diamond
  centered at (x,y).
• (eg) the pixels with D4 distance 2 from (x,y)
  (the center point) form the following contours of
  constant distance
• 2
• 2 1 2
• 2 1 0 1 2
• 2 1 2
• 2
• The pixels with D4 1 are the 4-neighbors of
  (x,y).

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D8 distance

• The D8 distance (called chessboard distance)
  between p and q is defined as
• D8(p,q) max( x s, y t).
• The pixels with D8 distance from (x,y) less than
  or equal to some value r form a square centered
  at (x,y).
• (eg) the pixels with D8 distance 2 from (x,y)
  (center point) form the following contours of
  constant distance
• 2 2 2 2 2
• 2 1 1 1 2
• 2 1 0 1 2
• 2 1 1 1 2
• 2 2 2 2 2
• The pixels with D8 1 are the 8-neighbors of
  (x,y).