Image Processing - Representing Digital Image


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Image Processing - Representing Digital Image

  1. 1. October 7, 2013 1
  2. 2. October 7, 2013 2 1. The Electromagnetic Spectrum 2. Images are Analog 3. Sampling 4. Quantization 5. Computer Representation of Images 6. Coordinate system 7. Pixel 8. Image Classification 9. Digital Image Types 10. Megapixels 11. Digital images - bit depth 12. Sample Depth 13. How do we Use these Pixels? 14. Digital image processing and operations with matrices 16. Image Resolution 15. Resolution 17. Spatial and Gray-Level Resolution 18. Spatial Resolution by Re-sampling 19. Spatial Resolution and Pixel Count 20. Gray Level Resolution
  3. 3. “Virtual image, a point or system of points, on one side of a mirror or lens, which, if it existed, would emit the system of rays which actually exists on the other side of the mirror or lens.” Clerk Maxwell
  4. 4. October 7, 2013 4 The Electromagnetic Spectrum
  5. 5. October 7, 2013 5  Relationship between frequency ( ) and wavelength ( ) , where c is the speed of light  Energy of a photon , where h is Planck’s constant     c  hE 
  6. 6. October 7, 2013 6 • Notice that we defined images as functions in a continuous domain. • Images are representations of an analog world. • Hence, as with all digital signal processing, we need to digitize our images. Images are Analog •Digitalization of an analog signal involves two operations: Sampling, and Quantization. • Both operations correspond to a discretization of a quantity, but in different domains.  a natural image is typically represented by a continuous or analog signal (such as a photograph, video frame, etc.) Samples = pixels Quantization = number of bits per pixel
  7. 7. October 7, 2013 7 Example: Analog Thermometer The mercury (or alcohol) rises continuously in direct proportion to the temperature. What exactly is this reading?
  8. 8. October 7, 2013 8 Example: Digital Thermometer This reading is discrete. Some detail is lost in converting to digital information. What is the actual temperature?
  9. 9. October 7, 2013 9 Sampling Sampling corresponds to a discretization of the space. That is, of the domain of the function, into f : [1, ...,N] [1, ...,M] f t A sampled function
  10. 10. October 7, 2013 10 Thus, the image can be seen as matrix, The smallest element resulting from the discretization of the space is called a pixel (picture element). For 3-D images, this element is called a voxel (volumetric pixel).
  11. 11. October 7, 2013 11 Quantization Quantization corresponds to a discretization of the intensity values. That is, of the co-domain of the function. After sampling and quantization, we get f t 3 2 1 0 Quantization
  12. 12. October 7, 2013 12  digitizing samples the natural image into discrete components  each discrete sample is averaged to represent a uniform value for that area in the image
  13. 13. October 7, 2013 13  A picture function f(x,y) is a real-valued function of two variables, having values that are nonnegative and bounded  0 ≤ f(x,y) ≤ L-1 for all (x,y)  When a picture is digitized, a sampling process is used to extract from the picture a discrete set of samples, and then a quantization process is applied to these samples Computer Representation of Images
  14. 14. October 7, 2013 14 Coordinate system We need a coordinate system to describe an image, the coordinate system used to place elements in relation to each other is called user space, since this is the coordinates the user uses to define elements and position them in relation to each other.
  15. 15. October 7, 2013 15 w An image: a multidimensional function of spatial coordinates. w Spatial coordinate: (x,y) for 2D case such as photograph, (x,y,z) for 3D case such as CT scan images (x,y,t) for movies w The function f may represent intensity (for monochrome images) or color (for color images) or other associated values.
  16. 16. October 7, 2013 16 PIXEL  Pixel is a smallest component of digital image  Pixel is a color point of digital image  An image should be comprised of many Pixels.
  17. 17. October 7, 2013 17 Image classification Bitmap image A bitmap (or raster) image is one of the two major graphic types. Bitmap- based images are comprised of pixels in a grid. Each pixel or "bit" in the image contains information about the color to be displayed. Bitmap images have a fixed resolution and cannot be resized without losing image quality
  18. 18. October 7, 2013 18 Vector Image Vector graphics are made up of many individual objects. Each of these objects can be defined by mathematical statements and has individual properties assigned to it such as color, fill, and outline. Vector graphics are resolution independent because they can be output to the highest quality at any scale.
  19. 19. October 7, 2013 19 Binary images: images having only two possible brightness levels (black and white). Digital Image Types : Binary Image Each pixel contains one bit : 1 represent white 0 represents black
  20. 20. October 7, 2013 20 Digital Image Types : Intensity Image Intensity image or monochrome image each pixel corresponds to light intensity normally represented in gray scale (gray level).
  21. 21. October 7, 2013 21 Image Types : Index Image Index image: Each pixel contains index number pointing to a color in a color table
  22. 22. October 7, 2013 22 Color images: can be described mathematically as three gray scale images Digital Image Types : RGB Image each pixel contains a vector representing red, green and blue components.
  23. 23. October 7, 2013 23 Megapixels refer to the total number of pixels in the captured image, an easier metric is raster dimensions which represent the number of horizontal and vertical samples in the sampling grid. An image with a 4:3 aspect ratio with dimension 2048x1536 pixels, contain a total of 2048x1535=3,145,728 pixels; approximately 3 million, thus it is a 3 megapixel image. Megapixels
  24. 24. October 7, 2013 24 Digital images - bit depth The bit depth or radiometric resolution is the number of bits used to represent each pixel NotesRangeBits Binary image0-11 Typical grayscale image0-2558 High quality grayscale0-409512 Very high quality grayscale0-6553516 Floating point format0.0 – 1.032 24 bit true color (monitor)3× 0-2558+8+8
  25. 25. October 7, 2013 25 Sample Depth The values of the pixels need to be stored in the computers memory, this means that in the end the data ultimately need to end up in a binary representation, the spatial continuity of the image is approximated by the spacing of the samples in the sample grid. The values we can represent for each pixel is determined by the sample format chosen.
  26. 26. October 7, 2013 26
  27. 27. October 7, 2013 27 How do we Use these Pixels? The image size in pixels determines what we can do with this image - how it can be used, and if it is appropriate size for the intended use. There are two fundamental uses which cover almost every application: printing the image on paper (print a photo in a book, etc), or showing the image on a video screen (snapshots or web pages, etc). 1024x768 pixels. Video screens are dimensioned in pixels, and images are dimensioned in pixels. Inches are no factor at all on the video screen, then for sure we don't need an image larger than that video screen size
  28. 28. October 7, 2013 28 when we print digital images on paper, the paper is dimensioned in inches, but digital images are dimensioned in pixels. We print the image on paper at some printing resolution, which is specified in pixels per inch (ppi), which is simply a spacing of pixels on paper. The image size in pixels determines the size we can print it in inches on paper. For example, if we print 1800 pixels width at 300 ppi, then those 1800 pixels will cover 6 inches of paper, simply because 1800 pixels / 300 ppi = 6 inches
  29. 29. October 7, 2013 29 Digital image processing and operations with matrices
  30. 30. October 7, 2013 30 RESOLUTION  How quality of image  With the same size of picture  If high resolution, high memory is required to store data  If low resolution, less memory is required to store data  Its unit is call “point per inch”
  31. 31. October 7, 2013 31 Image resolution It is an umbrella term that describes the detail an image holds. The term applies to raster digital images, film images, and other types of images. Higher resolution means more image details Image Resolution Spatial resolution: The measure of how closely lines can be resolved in an image is called spatial resolution, and it depends on properties of the system creating the image, not just the pixel resolution in pixels per inch (ppi). For practical purposes the clarity of the image is decided by its spatial resolution, not the number of pixels in an image. In effect, spatial resolution refers to the number of independent pixel values per unit length. The spatial resolution of computer monitors is generally 72 to 100 lines per inch, corresponding to pixel resolutions of 72 to 100 ppi
  32. 32. October 7, 2013 32 Spatial and Gray-Level Resolution
  33. 33. October 7, 2013 33 Spatial Resolution by Re-sampling
  34. 34. October 7, 2013 34
  35. 35. October 7, 2013 35 Spatial Resolution and Pixel Count
  36. 36. October 7, 2013 36 Spatial Resolution and Pixel Size The image resolution and pixel size are often used interchangeably. In reality, they are not equivalent. An image sampled at a small pixel size does not necessarily has a high resolution. The following three images illustrate this point. The first image is a SPOT image of 10 m pixel size. It was derived by merging a SPOT panchromatic image of 10 m resolution with a SPOT multispectral image of 20 m resolution. The effective resolution is thus determined by the resolution of the panchromatic image, which is 10 m. This image is further processed to degrade the resolution while maintaining the same pixel size. The next two images are the blurred versions of the image with larger resolution size, but still digitized at the same pixel size of 10 m. Even though they have the same pixel size as the first image, they do not have the same resolution
  37. 37. October 7, 2013 37 24 816128 3264 256 Gray-Level Resolution
  38. 38. October 7, 2013 38 This term refers to the size of an image, usually in reference to a photo from a digital camera or camera phone. Megapixel means one million pixels. The resolution of digital cameras and camera phones is often measured in megapixels. For example, a two- megapixel camera can produce images with two million total pixels. Since pixels are usually square and form a grid, a 1-megapixel camera will produce an image roughly 1200 pixels wide by 900 pixels high.
  39. 39. October 7, 2013 39 Some well known optical illusions
  40. 40. October 7, 2013 40
  41. 41. October 7, 2013 41 One should be able to clearly differentiate between the lines and gaps in Figure if you can’t resolve the pattern in Figure, you might consider paying a visit to an ophthalmologist
  42. 42. October 7, 2013 42