Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The Properties of Images and Imaging Devices Group II of the Imaging Chain

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A simple black & white image is a volume of information! Two dimensions are spatial dimensions (cm for example) The other dimension is lightness/darkness Think of an image mathematically. x y y x gray level

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science x y y x gray level Three dimensional graphs are hard to understand.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science y x Contour Plot: Another way to represent 3 dimensional information Lines are regions of constant gray level

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The 3D graph and the contour plot are not used much in imaging science. Other graphical representations are more often used. One that is commonly used is the "Histogram"

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The Histogram A statistical way of looking at an image Step #1: Sample the image Divide it up into "pixels"

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Step #2: Look at the gray value of each "pixel" Gray Value: R = Gray Scale R = 1 is white R = 0 is black

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science We have cut the image into lots of pieces, called "pixels". We measure the gray value, R, for each patch. Step #3: Take the gray pixels out of the image.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Step #4: Sort the pixels from darkest to lightest. There are many pixels at this gray level. Only a few at these gray levels.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science R = 0R = 1 Number at a given R Each pixel in the image has its place in the stacks of rearranged pixels.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Step #5: Form a graph to represent the sorted pixels. 01 Number of pixels at a given R Each pixel in the image has its place in the stacks of rearranged pixels. R

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science If you use very small pixels, the graph becomes sharper. 01 Number of pixels at a given R R This is called the image Histogram.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The Image Histogram Has Many Uses Use #1: A way to describe Properties of an Image

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The Image Histogram Has Many Uses Use #1: A way to describe Image "Brightness" R N R N R N Average R = 0.2Average R = 0.47Average R = 0.78

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science R N R N Same Average R=0.47 Different Ranges Range = 1 Range = 0.2 Range = 0.7 R N

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Brightness (Average R) Contrast Range of R R N R N R N R N R N R N R N R N R N Vary Both Brightness AND Contrast A graph of graphs!! Brightness ContrastContrast

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Summary of Brightness & Contrast 1. These are properties of the image. 2. The Histogram is a way of quantifying Brightness and Contrast. 01 Number of pixels at a given R R

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The Image Histogram Has Many Uses Use #2 A way to describe Imaging Devices.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science The Image Histogram Has Many Uses Use #2: A way to describe Imaging Devices. R N R N Average R = 0.2Average R = 0.78 For example, a camera OriginalPhoto-copy

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Imaging Devices Change Brightness and Contrast R N R N The image you have The image you want to make An Imaging Device Camera, scanner, transmission line, computer, display monitor, printer, etc. Anything in Group II of the Imaging Chain InputOutput

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science R N R N The image you have The image you want to make An Imaging Device InputOutput Example: Adobe Photoshop Program

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science R N R N The image you have The image you want to make An Imaging Device Input Output Think of the imaging device as something that changes the histogram.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RoRo N RcRc N Original gray levels, R o Copy gray levels R c. An Imaging Device Input Output The Imaging Device is described by the way it transforms gray levels in histograms. RcRc RoRo

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science An Imaging Device Input R o Output R c RcRc RoRo This graph is called the Tone Transfer Function (TTF). The TTF is a characteristic of the Imaging Device. Different shape curves will produce output different histograms.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RoRo N RcRc N Original gray levels, R o Copy gray levels R c. An Imaging Device Input Output How to measure a TTF RcRc RoRo

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Original An Imaging Device Input Output How to measure a TTF Use an image with a very simple histogram. A gray scale has the same number of pixels at each gray level. RoRo RoRo N Compare the output values, R c, versus the input values, R o. RoRo RoRo N

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Original Output How to measure a TTF This R o becomes this R c RcRc RoRo Plot the output values, R c, versus the input values, R o. Pair up the input values, R c, with the output values, R o. The graph is the TTF of the device.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Device Property #1: Location of the TTF Curve RcRc RoRo

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RcRc RoRo Device #1 Device #2 Device #3 Property #1: Location of the TTF Curve Device #1 Device #2 Device #3

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RcRc RoRo Device #1 Device #2 Device #3 Location: Controls the brightness of the copy image. Device #1 Device #2 Device #3 Device #1 is most sensitive to brightness. It makes the copy brighter. Device #3 is least sensitive to brightness. It makes the copy darker.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Useful Metric of Device Sensitivity RcRc RoRo Locate the middle gray for the output copy: R c = Device Devices #1 #2 #3

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RcRc RoRo A Useful Metric of Device Sensitivity Next, locate the corresponding input values: R os Device Devices #1 #2 #3 Device R os #10.30 #20.50 #30.68

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RcRc RoRo A Useful Metric of Device Sensitivity It is useful to define an index of "sensitivity": S. Device Devices #1 #2 #3 S 1 =1.67 S 2 =1.00 S 3 =0.74 Device R os S # # # S = 1 2R os

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science S 2 =1.00 S 3 =0.74 RcRc RoRo Device #1 Device #2 Device #3 Sensitivity (location) : Controls the brightness of the copy image. Device #1 #2 #3 S > 1 increases brightness. S = 1 gives the same brightness. S < 1 decreases brightness. S 1 =1.67 Device R os S # # #

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Device Property #2: Slope of the TTF Curve RcRc RoRo

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RcRc RoRo Device #1 Device #2 Device #3 Property #2: Slope of the TTF Curve Device #1 Device #3 Device #2

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Useful Metric of Device Slope RcRc RoRo Locate the middle gray for the output copy: R c = Device Devices TTF

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Useful Metric of Device Slope RcRc RoRo Next, Draw a straight line through the point so that it matches the slope at that point Device Devices TTF

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Useful Metric of Device Slope RcRc RoRo Locate the points where the straight line crosses R c =0 and R c =1. Find the corresponding values of R o. Call these R o0 and R o Device Devices TTF Slope = 1 R o1 - R o0 R o0 = 0.40 R o1 = 0.60 Slope = Slope = 5.0

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Useful Metric of Device Slope RcRc RoRo Device Devices TTF Slope = 1 R o1 - R o0 Slope = 5.0 Call this slope the "Contrast" of the device, symbolized by Greek letter "gamma", .  = 1 R o1 - R o0  = 5.0 Or,  = 1 R o1 - R o0  = 5.0

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science RcRc RoRo Device #1 Device #2 Device #3 Device #1 Device #3 Device #2  > 1 increases brightness.  = 1 gives the same brightness.  < 1 decreases brightness. Device  #15.00 #21.00 #30.20

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Summary of the Device TTF Device S=1 and  = 1Output copy = Input Copy S>1 Output copy is brighter S<1 Output copy is darker  1Output copy has higher contrast  1Output copy has less contrast

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Summary of the Device TTF S>1  =1 S<1  =1 S=1  1 S=1  1 S>1  1 S<1  1 S>1  1 S<1  1

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science S<1  =1 S>1  =1 S<1  1 S>1  1 S>1  1S=1  1 S=1  1 S<1  1 A Summary ofSensitivity & Gamma

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Cautious Note: There are many ways to define indices of sensitivity and slope. There are many other names used instead of sensitivity and slope. For example, Adobe Photoshop uses, Brightness -100% to 0 to +100% (instead of sensitivity 1) For example, Adobe Photoshop uses, Contrast -100% to 0 to +100% (instead of gamma 1) In general, however, the TTF of most imaging devices are characterized by some index of location (sensitivity, brightness, etc.) and by some index of slope (gamma, contrast, etc.) Sensitivity Gamma

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Properties of the Image: (I) The Histogram A. Brightness (average R) B. Contrast (Range of R) (II) Others to be discussed later (sharpness, granularity, etc.) Note: Don't confuse the terms "brightness" and "contrast" as used here for the terms used by Adobe and others for location and slope of the TTF. We are using the terms as properties of the image, not properties of the imaging device.

Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Properties of the Imaging Device: (I) The TTF (Transforms the histogram) A. Sensitivity B. Gamma (II) Others to be discussed later (sharpening/blurring, noise, etc.) Note: All imaging devices are described by the TTF. Most devices are given an index of location defined from the TTF. Most devices are given an index of slope defined from the TTF. However: Different organizations use different definitions for location and slope. They also use different names for the TTF, the location, and the slope. Also, terms like "sensitivity", "gamma", "brightness", and "contrast" are in common use, but there is no universal agreement about how these terms should be applied. Thus, all four are used by different groups to mean many different things, both as device properties and as image properties. Be cautious and ask for clarification if you are not sure what is meant.