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Image Processing with Biomedical
Applications
ELEG-475/
Prof. Barner
Image Processing Introduction Prof. Barner, ECE Department, University of Delaware 2
Course Materials & Evaluation
Books
Digital Image Processing, Gonzalez & Woods Introduction to the Mathematics of Medical Imaging, Epstein
Evaluation
Tests: midterm and final Homework and small projects Final independent research project
Independent reading – Ch. 1, Introduction
Imaging Fundamentals
Image Processing with Biomedical Applications ELEG-475/ Prof. Barner
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 4
Structure of the Human Eye
Enclosing membranes: Outer – cornea, sclera Choroid Retina Iris opening (2-8 mm) Retina light receptors Cones in fovea 6-7 million color sensitive Photopic (bright-light) vision Rods 75-150 million Not color sensitive Scotopic (low-light) vision
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 5
Distribution of Rods and Cones
Fovea Size: approximately 1.5 mm x 1.5 mm Cone density: approximately 150,000 elements per mm 2
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 6
Focal Length
Focal length distance between lens center and retina Approximately 14-17 mm By geometry, the image in the above example is 2.55 mm high on the retina Falls primarily in the fovea
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 7
Brightness Adaptation and Discrimination
Light sensitivity range: 10 10 Subjective (perceived) brightness logarithmic Entire range cannot be perceived simultaneously Brightness adaptation Photopic (cone) range is greater than scotopic (rod) range
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 8
Weber Ratio
Ability to discriminate between changes in light intensity Flat field I Short duration increment ∆ I Record 50% discrimination point Brightness discrimination is poor at low levels of illumination Rods have better discrimination
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 13
Electromagnetic Spectrum
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 14
Wavelength, Frequency, and Energy
Wavelength (λ) and frequency (ν) relation:
where c is the speed of light (2.998x10 8 m/s) Energy (electron-volts) is given by
where h Planck’s constant Electromagnetic waves can be visualized as: Propagating sinusoidal waves A stream of massless particles (photons) moving at the speed of light Higher frequency photons possess more energy Gamma rays are dangerous while radio waves are not
λ = c /ν
E = hv
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 15
Radiance and Luminance
Monochromatic (achromatic) light is void of color Intensity (gray level) is the defining attribute Radiance is the total energy that flows from a light source Luminance is the level of energy and observer perceives from a light source
Fundamental limit: To see an object the electromagnetic wavelength must be no bigger than the object To image molecules far ultraviolet or soft x-ray waves must be used
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 16
Image Acquisition
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 17
Various Acquisition Methodologies
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 18
Digital Image Acquisition
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 19
Simple Image Formation Model
An image is proportional to the radiated
energy
Illumination bound: Reflectivity bound: Transmission cases (x-ray): transmissivity rather than reflectivity Frequency dependent functions
f ( , x y ) = i x y r x y ( , ) ( , )
0 < i x y ( , )< ∞
0 < r x y ( , ) < 1
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 20
Sampling and Quantization
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 25
Spatial Resolution (Fixed Image Size)
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 26
Grade Level Resolution
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 27
Resolution and Image Detail
Resolution requirements are detail-level dependent
Isopreference curves give ( N,k) pairs that produce equal subjective quality Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 28
Isopreference Curves
Subjective quality for detailed images depends primarily on spatial resolution Low detail images are sensitive to the number of gray levels
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 29
Aliasing and Moire Patterns
Shannon Sampling Theorem: signals must be sampled at a rate at least twice the highest frequency to avoid aliasing
Paradox Only infinite time duration signals may be band-limited Finite time duration signals have infinite bandwidth No practical signals are band-limited
Special case: periodic signals can be preserved by sampling over a finite interval The sampling must capture an integer number of periods
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 30
Moire Pattern Effect
Each grate is periodic Their superposition breaks the periodicity Aliasing occurs The problem is common in scanning of printed material Periodicities do not line up causing aliasing
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 31
Image Zooming and Shrinking
Both operations involve resampling Zooming is oversampling Shrinking is undersampling
Nearest neighbor interpolation Overlay two sampling grids (known and unknown) Populate unknown grid with the closest sample from unknown grid Special case: pixel replication Integer increases in sampling rate Repeat rows, columns, etc.
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 32
Bilinear Interpolation
Unknown pixels are formed as a (distance) weighted sum of the four closest known pixels
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 37
Adjacency Example II
Consider the 4-, 8-, and m-paths of this figure Binary case, V ={1}
Under what connectivity are the 45° and -45° lines distinct?
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 38
Paths, Regions, and Boundaries
A path is closed if p^0 =p N Let S be a subset of pixels in an image p and q are connected in S if there exists a path between them consisting entirely of pixels in S For any p in S , the set of pixels connected to p in S is the connected component of S S is a connected set if it has only one connected component Connected subsets are referred to as regions The boundary of a region R is the set of pixels in the region that have one or more neighbors outside R Boundaries form closed paths (different concept than edge)
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 39
Distance Measures
Let p, q, and z be pixels. D is a distance functions (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 )
Euclidean distance: D (^) e ( p,q)= [( p (^) c1 -q (^) c1 )^2 + ( p (^) c2 -q (^) c2 )^2 ]½
City-block distance: D 4 ( p,q)= | p (^) c1 -q (^) c1 |+ | p (^) c2 -q (^) c2 |
Chessboard distance: D 8 ( p,q )=max(| p (^) c1 -q (^) c1 |, | p (^) c2 -q (^) c2 |)
Image Processing Imaging Fundamentals Prof. Barner, ECE Department, University of Delaware 40
Distance examples
D 4 example: 2 2 1 2 2 1 0 1 2 2 1 2 2 D 8 example:
D (^) m distance is defined as the length of the shortest m -path
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
