Digital Image Processing in Life Sciences
March 14th, 2012
Lecture number 1: Digital Image Fundamentals
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Terms to be conveyed:
Pixel
Gray level
Bit depth
Dynamic range
Connectivity types/neighborhood
Interpolation types
Look-up tables
Book:
Digital Image Processing, Rafael C. Gonzales and Richard E.Woods
Web resources:
www.microscopy.fsu.edu (very thorough and informative)
www.cambridgeincolour.com (beautiful examples, excellent tutorials)
Next topics:
2. Image enhancement in the spatial domain
3. Segmentation
4. Image enhancement in the frequency domain
5. Multi dimensional image processing
6-7. Guest lectures-TBD
What Is A Digital Image?
Image= “a two-dimensional function, f(x,y), where x and y are spatial
coordinates, and the amplitude of f at any pair of coordinates (x, y) is
called the intensity (gray level of the image) at that point. When x, y, and
the amplitude values of f are all finite, discrete quantities, we call the
image a digital image.” (Gonzalez and Woods).
These sets of numbers can be depicted in terms of frequencies
http://cvcl.mit.edu/hybrid_gallery/gallery.html
Digital Image Processing-Points to consider:
Why process?
Are both the input and output of a process images?
Where does image processing stop and image analysis start?
Are the processing results intended for human perception or for machine perception?
Character recognition and fingerprint comparisons vs intelligence photos…
We can define three types of computerized processes:
Low-, mid-, and high-level.
Low: image preprocessing, noise reduction, enhance contrast etc.
Mid: segmentation, sorting and classification.
High: assembly of all components into a meaningful coherent form
Digital image originsThe digital image dates back to…
the 1920’s and the Bartlane cable picture transmission system between NY and
London. The image took 3 hours to transmit, instead of more than one week.
They started with 5 tone levels and increased to 15 levels by 1929.
Taken from Gonzalez and Woods
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Essential steps when processing digital images:
Acquisition
Enhancement
Restoration
Outputs are
digital images
Color image restoration
Wavelets
Morphological processing
Segmentation
Representation
Recognition
Outputs are
attributes of
the image
Image acquisition
Acquire or receive an image for further processing.
This step has a major impact over the entire procedure of processing and
analysis.
Image Enhancement
Improving quality subjectively (e.g. by change of contrast)
Image Restoration
Improving quality objectively (e.g. by removing psf)
microscopy.fsu.edu
microscopy.fsu.edu
microscopy.fsu.edu
Morphological processing
Extracting components for the purpose of representing shapes
Segmentation
Deconstructing the image into its constituent objects. A crucial step for
successful recognition of the image contents.
Morphological processing
Extracting components for the purpose of representing shapes
Segmentation
Deconstructing the image into its constituent objects. A crucial step for
successful recognition of the image contents.
Representation
Feature selection-classification/grouping of objects
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Sampling and quantization
Keep in mind:
The sensor we used to create the image has a continuous output.
But, the transition from a continuum to a digital image requires two processes:
sampling and quantization.
Sampling is the process of digitizing the spatial coordinates.
Quantization is the process of digitizing the amplitude values at those spatial
coordinates.
The arrangement of the sensor used to create the image determines the sampling
method and its output.
Different limits determine the performance of the optical sensors and of the
mechanical sensors.
Sampling and quantization result in arrays of discrete quantities.
By convention, the coordinate (x,y)=(0,0) is located at the upper leftmost
corner of the image.
(Gonzales and Woods)
picture elements=image elements=pels=pixels
Sampling results in typical image sizes that can vary from 128 x 128 to 4096 x
4096 or any combination thereof.
An Image Formation Model
Let l(x0, y0) be the gray level (gl) value at (x0, y0) : l=f (x0, y0)
l is bounded by Lmin and Lmax and the boundary [Lmin, Lmax] is the gray scale.
This interval is usually shifted to [0, L-1] where 0 represents black gl values,
and L-1 represents white gl values.
Quantization results in discrete values of gray levels, typically an integer power of
2: L=2k .
If k=8, the result is 256 gray levels, from 0 to 255.
Dynamic range- the portion of the gray levels in the image out of the entire gray
scale of the image.
Think about high vs low dynamic range images: how does the dynamic range
affect the contrast of the image? Next lecture…
How many bits are required to save a digital image?
b=M x N x k (or M2k for images of equal dimensions).
Resolution
Size (kb)
Gray level (bit-depth)
8 (256)
12 (4096) 16 (65536)
128
16.384
24.576
32.768
256
65.536
98.304
131.072
512 262.144 393.216
524.288
1024 1048.576 1572.864 2097.152
2048 4194.304 6291.456 8388.608
8bit images- values are integers, unsigned
16bit images- values are integers, some softwares allow signed.
32bit images-floating-point, signed.
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Spatial and gray-level resolution
Spatial resolution is rather intuitive, and is determined by the quality and “density” of
the sampling.
Sampling theories (eg Nyquist-Shannon) state that sampling should be performed at
a rate that is at least twice the size of the smallest object/highest frequency.
Based on this, over-sampling and under-sampling (=spatial aliasing) can occur.
Gray level resolution is a term used to describe the binning of the signal rather than
the actual difference we managed to obtain when we quantized the signal. 8-bit and
16-bit images are the most common ones, but 10- and 12-bit images can also be
found.
Changing the resolution of the image without changing bit-depth
checker board patterns
512 x 512
256 x 256
128 x 128
64 x 64
Changing the bit-depth of the image without changing resolution
False contouring
8bit
4bit
3bit
2bit
1bit
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Neighbors of a pixel
(x-1, y-1) (x, y-1) (x+1, y-1)
(x-1, y)
(x,y)
(x+1, y)
(x-1, y+1) (x, y+1) (x+1, y+1)
(x+1, y), (x-1, y), (x, y+1), (x, y-1)= 4 neighbors of p, or N4(p)
(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1)= the four diagonal neighbors, or Nd(p).
N4(p) together with Nd(p) are N8(p).
Consider the case of image borders.
Adjacency/Connectivity, Regions, and Boundaries
Pixels are said to be connected if they are neighbors and if their gray levels
satisfy a specified criterion of similarity.
Consider this example of binary
pixels
V- the set of gray levels used to define adjacency. In this binary example, V={0}
to define adjacency of pixels with the value 0. In non-binary images, the values
of V can have a wider range.
The region R of an image- a subset of pixels which is a connected set, meaning that
there exists a path that connects the adjacent pixels.
The boundary (=border=contour) of R is the set of pixels in R that have one or more
neighbors that are not in R.
What happens when R is the entire image?
Do not confuse boundary with edge. The edge is formed by discontinuity of gray
levels at a certain point.
In binary images, edges and boundaries correspond.
Distances between pixels
Between (x,y) and (s,t):
Eucladian distance: given by Pythagoras
D4 distance (=city-block distance): D4(p, q) = |x – s| + |y – t|.
Pixel coordinates:
1,3
3,1
2
2,2
3,2
4,2
2,3
3,3
4,3
2,4
3,4
4,4
3,5
5,3
2
2
1
1
0
2
1
2
1
2
2
Diamond pattern
2
D8(p, q) =max( |x – s| , |y – t|) results in a square pattern around the center pixel.
2
2
2
2
1
1
2
1
0
2
1
1
2
2
2
2
1
1
1
2
2
2
2
2
2
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Zooming and shrinking digital images
Zoom: 1. Create new pixel locations
2. Assign gray level values to the locations
For increasing the size of an image an integer number of times, the
method of “pixel replication” is used.
For example, when changing a 512 x 512 image to 1024 x 1024, every
column and every row in the original image is duplicated.
At high magnification factors, checkerboard patterns appear.
Nearest neighbor interpolation
Bilinear interpolation (2 x 2)
Bicubic interpolation (4 x 4)
Examples of non-adaptive interpolation
Scaling up using different methods
Pixel replication
Bilinear
Bicubic
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
Look up tables:
Save computational time (LUTs can be found early in history…)
Require a mapping or transformation function- an equation that converts the
brightness value of the input pixel to another value in the output pixel
Do not alter pixel values
Image transformations that involve look-up tables can be implemented by either
one of two mechanisms: at the input so that the original image data are
transformed, or at the output so that a transformed image is displayed but the
original image remains unmodified.
www.microscopy.fsu.edu
Lecture’s outline
What Is Digital Image Processing?
(The Origins of Digital Image Processing)
Fundamental Steps in Digital Image Processing
Image Sampling and Quantization
Spatial and Gray-Level Resolution
Some Basic Relationships Between Pixels
Zooming and Shrinking Digital Images
Lookup tables
Color spaces
There are ways to describe color images other than the RGB space
Color space=color gamut
RGB= 3 X 8-bit channels= 24bit= true color
The histograms of RGB images can be viewed either as separate channels or as
the weighted average of the channels.
Some representations of color images calculate a weighted average of green,
red and blue.
Hue-Saturation-Intensity (more intuitive, as we perceive the world):
Hue= color spectrum, Saturation= color purity, Intensity= brightness
More: Hue-Saturation-Lightness; Hue-Saturation-Brightness
End of Lecture 1
Thank you!