# Image and Multidimensional Signal Processing

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1 Image and Multidimensional Signal Processing Professor William Hoff Dept of Electrical Engineering &Computer Science

2 Digital Image Fundamentals 2

3 Digital Image Fundamentals Topics Image acquisition and formation Resolution and size of objects Spatial sampling and quantization Matlab exercises Objectives Know how to estimate properties of image acquisition and formation, such as resolution and the size of objects that can be discerned Be familiar with the effects of spatial sampling and quantization on the quality of an image and its storage size 3

4 Notes: Eyeball is about 20 mm in diameter Retina contains both rods and cones Fovea is about 1.5 mm in width, contains about 337,000 cones Focal length about 17 mm 4

5 Rods sensitive to low light (scotopic vision) Cones detect color, work in bright light (photopic vision) 5

6 Image Formation h Treat as pinhole camera good approximation Similar triangles H f h What is the size of the tree on the retina? What if the tree were twice as far away? 15/100 = h/17 or h=2.55 mm 6

7 Problem 2.1 Assume the retina Contains 337,000 sensor elements arranged in a square array, 1.5x1.5 mm And the space between cones is equal to width of cone Estimate the diameter of the smallest printed dot that the eye can discern if the page on which the dot is printed is 0.2 m away from the eyes Assume the visual system ceases to detect the dot when the image of the dot on the fovea becomes smaller than the diameter of one receptor (cone) in that area of the retina 7

8 8

9 Light and the Electromagnetic Spectrum Wavelength (l) and frequency (n) are related by l c To resolve an object, we must use a wavelength equal to the size of the object or smaller 9

10 10

11 CCD (Charge coupled device) A 2D array of photosensitive transistors Charge accumulates during exposure Charges are transferred out to shift registers, read out sequentially Output is an analog signal (eg. RS-170, NTSC, PAL format) Can also be digitized and output in digital (via Firewire, USB, etc) 11

12 Typical CCD cameras Example: Panasonic GP-MF130 Sensor is 6x5 mm, 768x494 pixels Typical lens ~ 6mm focal length Field of view (see next slide)? 12

13 f = focal length q = field of view h = image plane size Field of View q/2 H/2 Center of projection f Image plane h/2 D Object plane being imaged tan(q/2) = (h/2) / f = (H/2) / D Horizontal field of view: tan(q/2) = (6mm/2) /(6mm) = 0.5 q = 2 arctan(0.5) = 53 degrees f, h can be in pixels or mm Horizontal, vertical fov could be different 13

14 Image Acquisition Using Sensor Strips Images can also be formed from (a) A linear array of sensors that is swept (b) A circular array, where the object is moved 14

15 Example Satellite Camera NOAA weather satellite KLM series for polar (low Earth) orbits 15

16 Image Formation 1 ), ( 0 ), ( 0 ), ( ), ( ), ( y x r y x i y x r y x i y x f Components Illumination i(x,y) Reflection r(x,y) 16

17 Sampling and Quantization N bits per pixel allows 2^N values 17

18 Examples An image has 8 bits per pixel If unsigned, range of values is? If signed (ie., two s complement), range is? Number of bytes in a 3872 x 2592 pixel image? 18

19 19

20 Image Representation Image can be represented by an xy plane Sampling partitions the plane into a grid of pixels, whose indices are integers We can also think of it as an MxN matrix of numbers We can index an element either by (row,col) or (x,y) (1,1) row (or y im ) col (or x im ) Image We will use the convention Top left pixel is (1,1) x index (or column) increases to the right y index (or row) increases down 20

21 Summary In digital cameras, the image is projected onto a 2D array of sensor elements. The image is (spatially) sampled by the sensor elements, and the intensities are quantized into discrete values. We can use the pinhole camera model to estimate the field of view and the size of objects projected onto the image. 21

22 Questions About how small an object can you see, using (a) visible light, (b) X-rays, or (c) microwaves? How does the human eye compare with a digital camera (e.g., in terms of resolution and sensitivity)? How could you measure the focal length of a camera? What units can it be expressed in? 22

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