1. 02-Gray Scale Control TTF

2. A TTF tells us how an imaging device relates the gray level of the input to the gray level of the output. P L Luminance, L pixel value, P

3. Luminance, L pixel value, P The TTF may be in the form of a graph, equation, or Look-Up-Table (LUT). P L L 0 10 20. 100 110 120. 300 P 0 1. 100 110 120. 255 becomes

4. pixel value, P (in the camera & sent to monitor) Original Luminance, L o An Imaging System involves Multiple imaging devices (TTFs) and Multiple kinds of images (types of gray) Luminance & Reflectance Irradiance, I (at the sensor) Luminance Note: We can't see a digital image. we see a copy of the digital image displayed on a monitor or printed on a printer. TTF(P vs L o ) (camera) TTF(L vs P) (monitor)

5. Luminance, L pixel value, P P L TTFs have many alternative names DLogH curve Characteristic curve Profile Tone curve I/O function ……etc. A successful imaging device must be designed with an appropriate TTF.

6. To understand the TTF of an imaging device, we first need to understand the gray scale properties of images. A printed, black & white image has gray values described as reflectance, R, decimal fractions from 0…1. A digital image has gray values described as pixel values, P, typically integers from 0…255.

7. Consider a hard copy image with gray values R (reflectance factor) from 0 to 1. Each location in the image (x,y) has a gray value R. x y

8. Gray levels, R, can be represented in a 3D graph. x y y x R However, this 3D graph isn't of much use.

9. So, we re-organize the gray values as follows. We call this graph a gray level Histogram.

10. The histogram tells us the properties of the gray level image. 01 Number of pixels R

11. For example, the point where the histogram balances is the "average" gray level of the image. has an average gray value of R=0.47.

12. The average value tells us the lightness/darkness of the image. Bright Image Dark Image

13. The width of the histogram tells us the contrast of the image. Lightness and Contrast are the two most common descriptions of the gray characteristics of an image. High Contrast Low Contrast R N 0 1 R N 0 1 R N 0 1

14. Digital images are described the same way. Lightness and Contrast are the two most common descriptions of the gray characteristics of any image. High Contrast Low Contrast P N 0 255 P N 0 P N 0

15. There are many metrics for image contrast. Most are based on the maximum and minimum values in the histogram. There are two ways to show the range between P max and P min. NN N P 0 255 P 0 P 0 P min P max (1) The contrast ratio: C = P max /P min (2) The contrast difference:  P = P max - P min (also called the "window") window

16. Printed images can be described in terms of Reflectance or Density. I o I printed image R ≡ I o / I and D ≡ -Log(R) A Rule of Thumb for Contrast Metrics: A ratio is used for describing things proportional to power. A difference is used for describing things proportional to Log(power) I is proportional to power.

17. Printed images can be described in terms of Reflectance or Density. I o I printed image I is proportional to power. Note that  D ≡ D max - D min = [-Log(R min ) ] - [-Log(R max ) ] = Log(R max ) - Log(R min ) = Log(R max /R min ) = Log(C) Two ways to describe image contrast: (1) C = R max /R min (2)  D = D max - D min R ≡ I o / I (R is proportional to power) and D ≡ -Log(R) (D is proportional to Log(power) )

18. "Dynamic Range": Printed Image I o I printed image Two ways to describe image contrast: (1) C = R max /R min (2)  D = D max - D min R ≡ I o / I (R is proportional to power) and D ≡ -Log(R) (D is proportional to Log(power) (1) C is often called the "Contrast Ratio" (2)  D is often called the "Dynamic Range" (Dr =  D)

19. L ≡ luminance in cd/m 2 L max and L min Image contrast is in terms of the maximum and the minimum luminance in the image. Contrast Ratio: C=L max /L min Dynamic Range: Dr = Log(C) "Dynamic Range": Monitor (soft) Image

20. Hard Copy Soft Copy Original Scene Contrast metrics of the Scene/Image L max L min L max L min D max R min D min R max "Image Contrast Ratio" C = L max /L min or C = R max /R min "Image Dynamic Range" Dr = Log(C) Note: These are contrast metrics of the Images, not the imaging devices that produced them. (See later)

21. Caution: There are many other metrics in common use to describe the gray scale properties of images. Many are industry or profession specific. Many are only loosely defined.

22. For example, professional photographers often use the term "Key" of an image. High "Key" Low "Key"

23. "Key is a characteristic of a "PROPERTLY" exposed image (subjective). Lightness is adjusted until a "PROPER" image is obtained. Then Key can be expressed in terms of the average gray level. Low "Key"

24. High "Key"

25. NOT low "Key", but an under exposed image. Learn the language of your customers!! Don't tell them they are "wrong" if their favorite metric is subjective.

26. Tone Characteristics of an Imaging Device

27. An imaging device changes one image into another. original L copy, P The tone characteristic of the imaging device is described by the TTF P L TTF of a camera transforms the the original histogram into the copy histogram. L N 0 0 P N 0 0

28. Tone Characteristics of an Imaging Device Just as the tone characteristics of an image are fully described by the histogram…………… original L copy, P …the tone characteristics of the imaging device are fully described by the TTF. P L L N 0 0 P N 0 0

29. Tone Characteristics of an Imaging Device Just as the tone characteristics of an image are partially described by metrics extracted from the histogram (contrast ratio, dynamic range, etc.)… original L copy, P …the tone characteristic of the imaging device partially described by metrics extracted from the TTF. P L L N 0 0 P N 0 0

30. Tone Characteristics of an Imaging Device original L copy, P L N 0 0 P N 0 0 Metrics of the TTF are defined differently for the three major types of imaging devices: (1) Image Capture Devices (camera, scanner, etc.) (2) Digital Image Processor (computers and chips) (3) Display Devices (printers, monitors, etc.)

31. Original Image Copy Image A computer is a commonly used DIP. It transforms one digital image into another digital image. PcPc 0 255 0 PoPo PcPc PoPo PoPo PcPc (2) Digital Image Processor (DIP)

32. Original Image Copy Image PoPo PcPc DIPs Commonly provide simple controls for (1) Brightness and (2) contrast = Brightness = Lightness/Darkness = Level = Contrast = Window

33. The most common TTF that is provided in DIPs such as ImageJ and PhotoShop is a simple straight line. P c =  ∙ P o + i or P c =  ∙(P o - j) + 128 Original Image Copy Image PoPo PcPc 0 255 PoPo 0 PcPc PoPo PcPc 0 0 Slope  and intercept, i PoPo PcPc 0 255 0 Slope  and center location, j

34. PoPo PcPc 0 255 0 Shifting the curve to the left is a brightness increase. The left/right location is called either "brightness", "lightness", or "level". Original Image Copy Image PoPo PcPc 0 255 PoPo 0 PcPc Shifting the curve to the left is equivalent to increasing the intercept.

35. PoPo PcPc 0 255 0 Original Image Copy Image PoPo PcPc 0 1 PoPo 0 1 PcPc Shifting the curve to the right is a brightness decrease. The left/right location is called either "brightness", "lightness", or "level".

36. PoPo PcPc 0 255 0  > 1 is a contrast increase. Original Image Copy Image PoPo PcPc 0 1 PoPo 0 1 PcPc window P c =  ∙ P o + i or P c =  ∙(P o - j) + 128 The slope is called either "contrast", "window", or "gamma".

37. The common digital TTF is a simple straight line. P 0 =  ∙ P c + i PoPo PcPc 0 255 0  < 1 is a contrast decrease Original Image Copy Image PoPo PcPc 0 1 PoPo 0 1 PcPc window

38. The Digital TTF Also called tone curve, profile, and LUT (look-up-table), point process Often, a much more complex TTF is needed. In that case, the TTF is not well described by two simple metrics.

39. The Digital TTF In "Threshold" Mode

40. Tone Characteristics of an Imaging Device original L copy, P L N 0 0 P N 0 0 Metrics of the TTF are defined differently for the three major types of imaging devices: (1) Image Capture Devices (camera, scanner, etc.) (2) Digital Image Processor (computers and chips) (3) Display Devices (printers, monitors, etc.)

41. Original Image Copy Image A printer converts pixel values, P, into reflection image density, D. D 0 3 0 255 PoPo P D = -Log(R) (3) Display Devices (printers, monitors, etc.)

42. Generate P=0,1,2,3……255 (all possible P values) D Use a densitometer to measure all possible output density values the printer can make. The printer TTF D P 0 255 D min D max printer convention monitor convention P=0,1,2,3……………… 255

43. The printer TTF D P 0 255 D min D max Printer Dynamic Range =  D = D max - D min (Looks like an image dynamic range!! But it is NOT the same.) Note that the printer dynamic range is expressed in terms of the density it CAN produce (D min and D max ). An image dynamic range is expressed in terms of its individual D min and D max.

44. Original Image Copy Image A monitor converts pixel values, P, into screen Luminance, L. L 0 255 PoPo P L (3) Display Devices (printers, monitors, etc.)

45. Generate P=0,1,2,3……255 (all possible P values) Measure all possible output Luminance values the monitor can make. The Monitor TTF L P 0 255 L min L max L printer convention monitor convention P=0,1,2,3……………… 255

46. Monitor Contrast Ratio C = L max - L min Monitor Dynamic Range = Log(C) (Looks like an image dynamic range!! But it is NOT the same.) Note that the monitor dynamic range is expressed in terms of the luminance it CAN produce (L min and L max ). An image dynamic range is expressed in terms of its individual L min and L max. The Monitor TTF L P 0 255 L min L max

47. Tone Characteristics of an Imaging Device original L copy, P L N 0 0 P N 0 0 Metrics of the TTF are defined differently for the three major types of imaging devices: (1) Image Capture Devices (camera, scanner, etc.) (2) Digital Image Processor (computers and chips) (3) Display Devices (printers, monitors, etc.)

48. (1) Image Capture Device (camera, scanner, etc.) Illuminance at sensor, I pixel value, P The TTF of the camera/scanner can be expressed in many ways: P vs R P vs L P vs I P vs H, where H= I∙ t P vs Log(H) object R reflected L R, L, I, H P It depends on the type of device and the specifications one wants to express.

49. (1) Image Capture Device (camera, scanner, etc.) Illuminance at sensor, I pixel value, P Or in terms of exposure, H = I∙t P vs R P vs L P vs I P vs H object R reflected L R, L, or I P

50. Film Camera: D Log(H) D max D min Log(H min )Log(H max ) Output Density Dynamic Range:  D = D max - D min Input Detection Contrast Ratio: C = H max /H min Input Detection Dynamic Range: Log(C) = Log(H max ) - Log(H min ) exposure, H = I∙t

51. The definition of Dynamic Range depends on defining D max, D min, H max, and H min. This means defining appropriate metrics of system noise.  H and  D. D Log(H) D max D min Log(H min )Log(H max ) Output Density Dynamic Range:  D = D max - D min Input Detection Contrast Ratio: C = H max /H min Input Detection Dynamic Range: Log(C) = Log(H max ) - Log(H min ) H max, and H min are the limiting values that are "meaningful" beyond the level of the noise. D max and D min are limiting D the film can make.

52. Digital Video Camera: P L P max = 255 P min = 0 L min L max Output Pixel Range:  = P max + 1 (number of discrete levels) Bit Depth = Log 2 (N) Input Detection Contrast Ratio: C = L max /L min Input Detection Dynamic Range: Log(C) = Log(L max ) - Log(L min ) Note: Bit Depth ≠ Camera Dynamic Range For a digital video camera the TTF is typically described as P vs L. Noise is a part of defining L min and L max.

53. Digital Still Camera: P H P max = 255 P min = 0 H min H max Output Pixel Range:  = P max + 1 (number of discrete levels) Bit Depth = Log 2 (N) Input Detection Contrast Ratio: C = H max /H min Input Detection Dynamic Range: Log(C) = Log(H max ) - Log(H min ) For a digital still camera exposure is H= I ∙t, and the TTF is often described as P vs H. Noise is a part of defining H min and H max. Exposure: H= I∙ t

54. Contrast Ratio, C = W max /W min Input Detection Dynamic Range: Log(C) But what kind of Logarithm do you use? Log is the "Common Logarithm"

55. Dynamic Range is defined using Logarithms of different bases, K. recall that Log K (C) = Log(C)/log(K) Log(C) = the regular base 10 logarithm of x. ln(C) = Log(C)/Log(e), called the natural log. Lg2(C) = Log(C)/Log(2) Db(C) = Log(C)/Log(10 0.1 ) called the decibel Db(C) = 10 ∙ Log(C) (another way to calculate Db) D(R) = log(R)/Log(0.1) D(R) = -1 ∙ log(R) (another way to calculate D) Common Log Natural Log Bits & Stops Decibel Density 10 e=2.718… 2 10 0.1 =1.259… 1/10 = 0.1 Name How to Calculate The base, K

56. End