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Digital Images Ho Kyung Kim [email protected] Pusan National University Introduction to Medical Engineering
Digital Images
Ho Kyung [email protected]
Pusan National University
Introduction to Medical Engineering
Outline
• digitization = space sampling + intensity quantization
• histogram
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Analog vs. digital
• Digitization = sampling (of space) + quantization (of signal intensity)
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Quantum & digital images
-10 -5 0 5 10x (mm)
10-6
10-4
10-2
100 a = 1 m a = 10 m a = 50 m a = 100 m
0 5 10 15
f (mm-1)
0.0
0.2
0.4
0.6
0.8
1.0 a = 1 m a = 10 m a = 50 m a = 100 m
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∆𝑎 10 𝜇𝑚 ∆𝑎 50 𝜇𝑚
Thanks to Junwoo for preparing this slide
-2 -1 0 1 2x (mm)
Sampling
• The conversion from a continuous function to a discrete function retaining only the values at the grid points
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17921792 896896 448448 224224
141428285656112112
128 larger pixel
Quantization
• The conversion from analog samples to discrete‐value samples
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8 bits 7 bits 6 bits 5 bits
1 bit2 bits3 bits4 bits
Digital images
• A set of possible (achromatic) gray levels or (chromatic) colors in a rectangular grid‐point (or pixel) array
• Sampling and quantization (integer)• Dynamic range: the set of possible gray levels• Contouring: an artificial looking height map• How many gray values are needed to produce a continuous‐looking image?
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8 bits/pixel 4 bits/pixel
• Consider an image expressed with 𝑛 1 gray values with intensities 𝐼 , 𝐼 , … 𝐼 , … , 𝐼
• Sometimes called the dynamic range = . .
• Human eye cannot distinguish subsequent intensities 𝐼 and 𝐼 if they differ less than 1% (i.e., 𝐼 1.01𝐼 )
– 𝐼 1.01 𝐼 or 𝑛 log . 𝐼 /𝐼• Therefore, for continuous looking brightness,
– 𝑛 463 (9 bits) for dynamic range = 100– 𝑛 694 (10 bits) for dynamic range = 1000
• Most digital medical images use 4069 gray values (12 bits per pixel)
• The problem with too many gray values is that small differences in brightness cannot be perceived on the display
– Gray value transformation (e.g., expanding a small gray value interval into a larger one)
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Histogram
• Consider a digital image w/ 𝐿 gray levels & the total number of pixels of 𝑁– 𝑟 = 𝑘‐th gray level & 𝑘 ∈ 0, 𝐿 1– 𝑛 = the number of pixels in the image having gray level 𝑟– Histogram is a discrete function, ℎ 𝑟 𝑛
– 𝑝 𝑟 , an estimate of the probability of occurrence of gray levels 𝑟
• Various representations
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10Taken from R. C. Gonzalez & R. C. Woods, Digital Imaging Processing (2002)
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Too bright Too dark
Example
It is known the Retina HD display has 1792 828‐pixel resolution at 326 ppi. Then, estimate the display dimension in millimeters.
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Example
When you take a picture using a 12M‐pixel camera ( 5000 2300 pixels), what is the image size?
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Digital image is a matrix
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Pixel (or picture element) value = 127
= a 14 14 matrix
0
255
0
127
255
Wrap‐up
• digitization = space sampling + intensity quantization– checkboard artifact– contouring artifact
• histogram– a representation of counting how many pixels correspond to each gray value
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