BIM472 Image processing

1
BIM472 Image processing

• Week 2

2
Contents

• Visual Perception
• Image Sensing and Acquisition
• Sampling and Quantization
• Representing Digital Images
• Zooming and Shrinking Digital Images
• Some Basic Relationships Between Pixels

3
Human Eye
4
Elements of Visual Perception

• When the eye is properly focused, light from an
  object outside the eye is imaged on the retina
• There are discrete light receptors on the retina
• There are two classes of receptors Cones and Rods

5
Cones

• Number of 6-7 million
• In the central portion of retina (which is called
  fovea)
• Highly sensitive to color
• Humans can resolve fine details by them
• Each one is connected to its own nerve end
• Cone vision is called photopic or bright-light
  vision

6
Rods

• Number of 75-150 millions
• Several nodes are connected to a single nerve
• Less detail is discernible by them
• Serve to give a general, overall picture of the
  field of the view
• Not involved in color vision
• Sensitive to low-level illumination
• We see colored-objects colorless at moonlight.
  This phenomena is called scotopic or dim-light
  vision

7
Fovea versus CCDs

• We can think fovea as 1.5 mm. 1.5 mm. with
  337,000 elements
• CCD can contain that number of receptors in an
  area of 5 mm. 5 mm.

8
Brightness Adaptation and Discrimination

• Real brightness and perceived brightness are a
  bit different
• Visual system tends to undershoot or overshoot
  around the boundary of regions of different
  intensities
• A regions perceived brightness does not depend
  simply on its intensity
• Optical illusions

9
Undershooting and Overshooting
10
Simultaneous Contrast
11
Optical Illusions
12
Light and EM Spectrum

• The colors that humans perceive in an object are
  determined by the nature of the light reflected
  from the object
• Electromagnetic spectrum was mentioned last week

13
Image Sensing and Acquisition
14
Image Sensing and Acquisition

• The most familiar sensor is photodiode
• Filter is used to improve selectivity (e.g. green
  light)

15
Single Sensor
16
Sensor Strips
17
Sensor Strips

• Scanners
• Photocopy machines
• Geographical imaging
• Medical imaging
• Industrial imaging

18
Sensor Arrays
19
Sensor Arrays

• Used in digital cameras
• Sensor array is called Charged-Coupled Device
  (CCD)
• In digital cameras there may be 4000 4000 CCDs

20
Sampling and Quantization

• Digitizing the coordinate values is called
  sampling
• Digitizing the amplitude values is called
  quantization
• Remember that images are represented by 2D
  function f(x,y)
• Digitizing x and y is called sampling
• Digitizing f is called quantization

21
Sampling and Quantization
22
Sampling and Quantization
23
Digitizing Digital Images
24
Digitizing Digital Images

• The number of gray levels typically is an integer
  power of 2 L 2k
• We assume that the discrete levels are equally
  spaced and that they are in the interval 0, L -
  1
• The number of bits required to store a digital
  image of size M N is b M N k

25
k-bit Image

• The images that have 2k gray levels is called
  k-bit images
• For example An image with 256 possible
  gray-level values is called an 8-bit image

26
Spatial and Gray-Level Resolution

• Spatial resolution is the smallest discernible
  detail in an image
• Gray-level resolution is the smallest discernible
  change in gray-level

27
Spatial Resolution
28
Spatial Resolution
29
Gray-Level Resolution
30
Gray-Level Resolution
31
Details in Digital Images
32
Zooming and Shrinking

• Nearest neighbor interpolation
• Example 500 500 ? 750 750
• Pixel replication
• Special case of nearest neighbor interpolation
• Example 500 500 ? 1500 1500
• Bilinear interpolation
• Uses four nearest neighbors

33
Bilinear Interpolation
34
Some Basic Relationships Between Pixels

• Neighbors of a pixel
• Adjacency
• Path
• Connectivity
• Region
• Boundary
• Edge
• Distance measures

35
Neighbors of a Pixel

• Let p be a pixel
• 4-neighbors of p is N4(p)
• Horizontal and vertical neighbors of p
• Diagonal-neighbors of p is ND(p)
• Diagonal neighbors of p
• 8-neighbors of p is N8(p)
• Both N4(p) and ND(p)
• Some neighbors may fall outside of image

36
Adjacency

• Let V be a set of gray-level values used to
  define adjacency
• If the gray-level values of two neighbor pixels
  are in V, then they are connected
• For binary images with values 0 and 1, V may be
  defined as V 1
• For gray-scale images, V may be any subset of all
  possible gray-level values
• For example V 250,251,252,253,254,255

37
Adjacency

• 4-adjacency
• p and q are 4-adjacent if q is in N4(p) and p and
  q have values from V
• 8-adjacency
• p and q are 8-adjacent if q is in N8(p) and p and
  q have values from V
• m-adjacency (mixed adjacency)
• p and q have values from V
• i) q is in N4(p) or ii) q is in ND(p) and
  the set N4(p)?N4(q) has no pixels whose values
  are from V

38
Adjacency
N4(p)?N4(q)
39
Adjacency Example
40
Adjacency

• Two image subsets S1 and S2 are adjacent if some
  pixel in S1 is adjacent to some pixel in S2
• Here, adjacent means 4-, 8-, or m-adjacent

41
Path

• A (digital) path (or curve) from p (x0 , y0) to
  q (xn , yn) is a sequence of distinct pixels
  with coordinates (x0 , y0), (x1 , y1), , (xn ,
  yn) and (xi , yi) and (xi-1 , yi-1) are adjacent
  for 1 i n
• Here, n is the length of the path
• If (x0 , y0) (xn , yn), the path is a closed
  path
• 4-path, 8-path and m-path are defined according
  to the adjacency

42
Connectivity

• Let S represent a subset of pixels in an image.
• Two pixels p and q are said to be connected in S
  if there exists a path between them consisting
  entirely of pixels in S.
• For any pixel p in S, the set of pixels that are
  connected to it in S is called a connected
  component of S.
• If S has only one connected component, then the
  set S is called a connected set.

43
Region

• Let R be a subset of pixels in an image.
• We call R a region of the image if R is a
  connected set.

44
Boundary

• The boundary (border or contour) of a region R is
  the set of pixels in the region that have one or
  more neighbors that are not in R.
• If R happens to be an entire image, then its
  boundary is defined as the first and last rows
  and columns of the image.
• The boundary of a finite region forms a closed
  path.

45
Edge

• An edge is a set of connected pixels that lie on
  the boundary between two regions.
• Edges are intensity discontinuities and
  boundaries are closed paths.

46
Distance Measures

• For pixels p(x,y), q(s,t) and z(v,w), D is a
  distance function or metric if
• a) D(p,q) 0 and D(p,q) 0 iff p q
• b) D(p,q) D(q,p)
• c) D(p,z) D(p,q) D(q,z).
• The Euclidian distance between p and q is defined
  as
• De(p,q) (x-s)2 (y-t)21/2

47
D4 and D8 Distances

• D4 distance is also called city-block distance
• D4(p,q) x s y t
• D8 distance is also called chessboard distance
• D8(p,q) max( x s , y t )

48
Using MATLAB for Image Processing
49
Image File Formats

• TIFF Tagged Image File Format
• JPEG Joint Photographic Experts Group
• GIF Graphics Interchange Format
• BMP Windows Bitmap
• PNG Portable Network Graphics
• XWD X Window Dump

50
Coordinate Conventions
51
Image Functions

• f imread(cameraman.tif)
• size(f)
• M, N size(f)
• imshow(f)
• imshow(f, low high )
• imshow(f, )
• pixval
• imshow(f) figure imshow(g)
• imwrite(f, newpicture.jpg)
• K imfinfo(cameraman.tif)

52
Image Types

• The toolbox supports four types of images
• Intensity images
• Binary images
• Indexed images
• RGB images

53
Intensity Images

• If the elements of an intensity image are of
  class uint8, or class uint16, then they have
  integer values in the range 0, 255 and 0,
  65535 respectively/
• If the image is of class double, the values are
  floating-point numbers and take the values in the
  range 0, 1.

54
Binary Images

• A binary image is a logical array of 0s and 1s.
• A numeric array is converted to binary using the
  function logical.

55
Converting between Image Classes

• im2uint8
• im2uint16
• mat2gray
• Converts double matrices to double images in the
  range 0, 1
• im2double
• im2bw
• Converts its input to logical image

56
Functions

• This program sums and subtracts
• two parameters
• function sum, diff myfunc(a, b)
• sum a b
• diff a - b
• return

Write this code into a file named myfunc.m
57
Exercises

• How can you flip an image vertically?
• How can you flip an image horizontally?
• How can you crop an image?
• How can you subsample an image (i.e. make
  smaller)?