Digital Image Fundamentals. Chapter Two Instructor: Hossein Pourghassem. Human Visual Perception
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1 Digital Image Fundamentals Chapter Two Instructor: Hossein Pourghassem Human Visual Perception 1
2 Human Visual Perception requires some knowledge of of how we we see see colors Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 3 Eye s Light Sensors cone density near fovea #(blue) << #(red) < #(green) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 4
3 The Human Eye Diameter: 0 mm 3 membranes enclose the eye.(صلبيه) & sclera (قرينه) Cornea.(استري) Choroid.(شبكيه) Retina Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 5 The Choroid The choroid contains blood vessels for eye nutrition and is heavily pigmented to reduce extraneous light entrance and backscatter. It is divided into the ciliary body and the iris diaphragm, which controls the amount of light that enters the pupil ( mm ~ 8 mm). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 6 3
4 The Lens The lens is made up of fibrous cells and is suspended by fibers that attach it to the ciliary body. It is slightly yellow and absorbs approx. 8% of the visible light spectrum. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 7 The Retina The retina lines the entire posterior portion. Discrete light receptors are distributed over the surface of the retina: cones (6-7 million per eye) and rods ( million per eye) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 8 4
5 Cones Cones are located in the fovea and are sensitive to color. Each one is connected to its own nerve end. Cone vision is called photopic (or bright-light vision). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 9 Rods Rods are giving a general, overall picture of the field of view and are not involved in color vision. Several rods are connected to a single nerve and are sensitive to low levels of illumination (scotopic or dimlight vision). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 10 5
6 Receptor Distribution The distribution of receptors is radially symmetric about the fovea. Cones are most dense in the center of the fovea while rods increase in density from the center out to approximately 0% off axis and then decrease. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 11 Cones and Rods Distribution Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 1 6
7 The Fovea The fovea is circular (1.5 mm in diameter) but can be assumed to be a square sensor array (1.5 mm x 1.5 mm). The density of cones: 150,000 elements/mm ~ 337,000 for the fovea. A CCD imaging chip of medium resolution needs 5 mm x 5 mm for this number of elements Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 13 Image Formation in the Eye The eye lens (if compared to an optical lens) is flexible. It gets controlled by the fibers of the ciliary body and to focus on distant objects it gets flatter (and vice versa). Distance between the center of the lens and the retina (focal length): varies from 17 mm to 14 mm (refractive power of lens goes from minimum to maximum). Objects farther than 3 m use minimum refractive lens powers (and vice versa). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 14 7
8 Image Formation in the Eye Example: Calculation of retinal image of an object 15 x = x =. 55mm Perception takes place by the relative excitation of light receptors. These receptors transform radiant energy into electrical impulses that are ultimately decoded by the brain. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 15 Brightness Adaptation & Discrimination Range of light intensity levels to which HVS (human visual system) can adapt: on the order of Subjective brightness (i.e. intensity as perceived by the HVS) is a logarithmic function of the light intensity incident on the eye. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 16 8
9 Brightness Adaptation & Discrimination The HVS cannot operate over such a range simultaneously. For any given set of conditions, the current sensitivity level of HVS is called the brightness adaptation level. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 17 Brightness Adaptation & Discrimination Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 18 9
10 Brightness Adaptation & Discrimination The eye also discriminates between changes in brightness at any specific adaptation level. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 19 Brightness Adaptation & Discrimination Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 0 10
11 Brightness Adaptation & Discrimination Small values of Weber ratio mean good brightness discrimination, and brightness discrimination is poor (the Weber ratio is large) at low levels of illumination. At low levels of illumination brightness discrimination is poor (rods) and it improves significantly as background illumination increases (cones). The two branches in the curve reflect the fact that at low levels of illumination vision is carried out by activity of the rods, whereas at high levels (showing better discrimination) vision is the function of cones. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 1 Brightness Adaptation & Discrimination Perceived brightness is not a simple function of intensity, for example: Scalloped effect (Mach band pattern), the visual system tends to undershoot or overshoot around the boundary of regions of different intensities. Simultaneous contrast (A region s perceived brightness does not depend simply on its intensity). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 11
12 Perceived Brightness Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 3 Simultaneous Contrast All the inner squares have the same intensity, but they appear progressively darker as the background becomes lighter. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 4 1
13 Optical Illusions Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 5 Electromagnetic Spectrum λ = c f E = hf Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 6 13
14 Image Sensor Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 7 Image Sensor (Single Sensor) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 8 14
15 Image Sensor (Sensor Strips) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 9 Digital Image Acquisition Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 30 15
16 A Simple Image Model Image: a -D light-intensity function f(x,y) The value of f at (x,y) the intensity (brightness) of the image at that point: 0 < f(x,y) < Nature of f(x,y): The amount of source light incident on the scene being viewed. The amount of light reflected by the objects in the scene. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 31 A Simple Image Model Illumination & reflectance components: Illumination: i(x,y) Reflectance: r(x,y) f(x,y) = i(x,y) r(x,y) 0 < i(x,y) < and 0 < r(x,y) < 1 (from total absorption to total reflectance) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 3 16
17 A Simple Image Model Sample values of r(x,y): 0.01: black velvet 0.93: snow Intensity of a monochrome image f at (xo,yo): gray level (l) of the image at that point, l=f(xo, yo) L min l L max Where L min : positive L max : finite Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 33 A Simple Image Model In practice: L min = i min r min and L max = i max r max E.g. for indoor image processing: L min 10 L max 1000 [L min, L max ] : gray scale Often shifted to [0,L-1] l=0: black l=l-1: white Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 34 17
18 Sampling & Quantization The spatial and amplitude digitization of f(x,y) is called: Image sampling when it refers to spatial coordinates (x,y) and Gray-level quantization when it refers to the amplitude. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 35 Digital Image Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 36 18
19 Sampling and Quantization Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 37 A Digital Image Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 38 19
20 Sampling & Quantization f (0,0) f (1,0) f ( x, y) =... f ( N 1,0) f (0,1) f ( N 1,1) f (0, M 1) f (1, M 1)... f ( N 1, M 1) Digital Image Image Elements (Pixels) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 39 Sampling & Quantization Sampling: partitioning xy plane into a grid the coordinate of the center of each grid is a pair of elements from the Cartesian product Z x Z (Z ) Z is the set of all ordered pairs of elements (a,b) with a and b being integers from Z. Z: set of real integers. R: set of real numbers. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 40 0
21 Sampling & Quantization f(x,y) is a digital image if: (x,y) are integers from Z and f is a function that assigns a gray-level value (from Z) to each distinct pair of coordinates (x,y) [quantization] Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 41 Sampling & Quantization The digitization process requires decisions about: values for N,M (where N x M: the image array) and the number of discrete gray levels allowed for each pixel (G). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 4 1
22 Sampling & Quantization Usually, in DIP these quantities are integer powers of two: N= n M= m and G= k number of gray levels Another assumption is that the discrete levels are equally spaced between 0 and L-1 in the gray scale. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 43 Sampling & Quantization If b is the number of bits required to store a digitized image then: b = N x M x k (if M=N, then b=n k) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 44
23 Storage Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 45 Sampling & Quantization How many samples and gray levels are required for a good approximation? Spatial resolution (the degree of distinguishable detail) of an image depends on the number of sample and gray level resolution depends on the number of gray level. i.e. the more these parameters are increased, the closer the digitized array approximates the original image. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 46 3
24 Sampling & Quantization How many samples and gray levels are required for a good approximation? (cont.) But: storage & processing requirements increase rapidly as a function of N, M, and k Different versions (images) of the same object can be generated through: Varying N, M numbers Varying k (number of bits) Varying both Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 47 Examples Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 48 4
25 Examples Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 49 Examples Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 50 5
26 Examples Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 51 Sampling & Quantization Isopreference curves (in the N-k plane) Each point: image having values of N and k equal to the coordinates of this point. Points lying on an isopreference curve correspond to images of equal subjective quality. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 5 6
27 Examples Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 53 Isopreference Curves Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 54 7
28 Sampling & Quantization Conclusions: Quality of images increases as N & k increase. Sometimes, for fixed N, the quality improved by decreasing k (increased contrast). For images with a large amount of detail only a few gray levels may be needed. (isopreference curves tend to become more vertical as the detail in the image increases). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 55 Aliasing and Moiré Patterns Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 56 8
29 Zooming and Shrinking Digital Images Zooming may be viewed as over-sampling, while shrinking may be viewed as under-sampling. Zooming requires two steps: the creation of new pixel locations, and the assignment of gray levels to those new locations. Nearest neighbor interpolation Bilinear interpolation. Cubic interpolation. Image shrinking is done in a similar manner as described for zooming. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 57 Example Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 58 9
30 Some Basic Relationships Between Pixels Definitions: f(x,y): digital image Pixels: q, p Subset of pixels of f(x,y): S Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 59 Neighbors of a Pixel A pixel p at (x,y) has horizontal and vertical neighbors: (x+1,y), (x-1,y), (x,y+1), (x,y-1) This set of pixels is called the 4-neighbors of p: N 4 (p) The 4 diagonal neighbors of p are: (N D (p)) (x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1) N 4 (p) + N D (p) N 8 (p): the 8-neighbors of p. Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 60 30
31 Region and Boundary Region: R a subset of pixels is a region if R is a connected set. Its boundary (border, contour) is the set of pixels in R that have at least one neighbor not in R Edge can be the region boundary (in binary images) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 61 Distance Measures For pixels p,q,z with coordinates (x,y), (s,t), (u,v), D is a distance function or metric if: D(p,q) 0 (D(p,q)=0 iff p=q) D(p,q) = D(q,p) and D(p,z) D(p,q) + D(q,z) Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 6 31
32 Distance Measures Euclidean distance: D e (p,q) = [(x-s) + (y-t) ] 1/ Points (pixels) having a distance less than or equal to r from (x,y) are contained in a disk of radius r centered at (x,y). Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 63 Distance Measures D 4 distance (city-block distance): D 4 (p,q) = x-s + y-t forms a diamond centered at (x,y) e.g. pixels with D 4 from p D 4 = 1 are the 4-neighbors of p 1 Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 64 3
33 Distance Measures D 8 distance (chessboard distance): D 8 (p,q) = max( x-s, y-t ) Forms a square centered at p e.g. pixels with D 8 from p D 8 = 1 are the 8-neighbors of p Islamic Azad University of Najafabad, Department of Electrical Engineering, Dr. H. Pourghassem, 65 33
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