Visual Perception, Image Formation, Math Concepts 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts References Gonzalez and Woods, “ Digital Image Processing,” 2nd Edition, Prentice Hall, 2002. Jahne, “Digital Image Processing,” 5th Edition, Springer 2002. Jain, “Fundamentals of Digital Image Processing,” Prentice Hall 1989 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Overview Human Visual System Visual Perception Image Acquisition Sampling and Quantization Basic pixel relationships 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts What are we looking for? The Human Visual System is complex. Need to find clues to “improve” image quality (from the viewpoint of the human). Our focus is on math techniques to achieve an objective. Which techniques are most appropriate? What is the impact of illumination? 11/20/2018 Visual Perception, Image Formation, Math Concepts

Cross Section of the Eye Two kinds of receptors Cones ~ 6 to 7 million Primarily in fovea Sensitive to color One cone per nerve end Bright light vision (photopic) Rods ~ 75 to 100 million Several rods / nerve end General overall picture of field of view Sensitive to low levels of illumination Dim light vision (scotopic) From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Some questions that helps Image Processing How many sensors are needed to “see” well? How does the eye adjust to brightness? What is the eye’s ability to discriminate between light intensity changes? 11/20/2018 Visual Perception, Image Formation, Math Concepts

Cones and Rods Distribution From [1] Rod, cone distribution is symmetric around the center of fovea, except the blind spot. Fovea is a circular indentation that is about 1.5mm diameter. Most sensing elements are rectangular, so to draw lessons treat the fovea to be 1.5 mm x 1.5 mm. Cone density is about 150K per mm2. Cones in fovea: 150K*1.5*1.5=337.5K. Modern 5mm x 5mm imaging sensors accommodate 300K detectors. 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts From [1] Eye lens is flexible – the focal length (distance between lens and the retina) varies from 17 to 14 mm. From similarity of triangles (h=height of image): h/17 = 15/100; h = 2.55 mm d f h x x = f h / d Object Pin-hole Image 11/20/2018 Visual Perception, Image Formation, Math Concepts

Brightness Adaptation HVS adapts to a 1010 range of light intensity. Subjective brightness (intensity as perceived by HVS) is log of the light incident on the eye. Gradual transition from Scotopic to Photopic. HVS does not operate over the entire range simultaneously. Small variations about an operating point. From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Discrimination If ΔI is small, no change perceived. ΔIc/I is Weber ratio; where ΔIc is the change that is detected 50% of the time. From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Mach bands From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Another example of contrast From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Electromagnetic Spectrum From [1] C = λν = 3 * 1010 cm/second The wavelength of the EM wave used to “see” must be smaller than the object size being detected. 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Measures of light Gray level is used to define monochromatic intensity. Black to white. Radiance: Light source measured in watts Luminance: Perceived amount of energy from light source Brightness: Subjective measure For IR: Radiance maybe high, but Luminance is zero. 11/20/2018 Visual Perception, Image Formation, Math Concepts

Different types of Sensors Filters are used to reduce the range of colors, e.g. green filters will only pass green incident energy. Used in Aerial sensors like FLIRS From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Linear and Circular sensors From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Sampling Rate? What is a good sampling rate? High rate will require more storage and communication cost Low rate – we may miss something Sampling rate should enable adequate reconstruction How to interpolate between samples – this figures into the sampling rate selection 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Reconstruction? 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Image Acquisition Quantized From [1] Sampled 11/20/2018 Visual Perception, Image Formation, Math Concepts

Image Formulation Model An image is represented as f (x, y, s) f is the value at the spatial co-ordinate x, y using a spectral frequency s (suppressed in the further analysis) 0 < f (x, y) < ∞ f (x, y) = illumination * reflectance = i (x, y) * r (x, y) 0 < i (x, y) < ∞ 0 < r (x, y) < 1 : 0 = absorption; 1=total reflectance 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Typical values i (x, y): Sun produces 90K lumens/sq.m. on a sunny day, and 10K on a cloudy day. Full moon yields about 0.1 lumens/sq.m Commercial building 1K lumens/sq.m. r (x, y): .01 for black velvet 0.65 for stainless steel 0.85 for flat white wall paint 0.91 for silver plated metal 0.93 for snow 11/20/2018 Visual Perception, Image Formation, Math Concepts

Steps in Digitizing an Image From [1] Quantization 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Quantization From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Representing Digital Images From [1] f(0,0) f(0,1) . . . . . f(0, N-1) f(1,0) f(1,1) . . . . . f(1, N-1) f(x,y) = . . . . . . f(M,0) f(M,1) . . . . . f(M, N-1) f(i,j) = integer 0 <= f(i,j) <= 2k 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Impact of sub sampling (zoom) From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Impact of reduced gray levels From [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts

Zooming using interpolation 11/20/2018 Visual Perception, Image Formation, Math Concepts

Basic Relationships between pixels 1 Neighborhoods of pixel p N4(p) = 4 nearest neighbors ND(p) = 4 diagonal neighbors N8(p) = 8-neighbors of p Connectivity 4, 8 and m connectivity Adjacency: if p, q are connected they are adjacent Distance metrics Euclidean, city-block, chess board 1 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts Adjacency Neighboring pixels are connected only if their value is similar, i.e. belongs to a set V If p and q have values in V, and 4-adjacent: q is in the set N4(p) 8-adjacent: q is in the set N8(p) m-adjacent: q is in the set N4(p) or q is in the set ND(p) and {N4(p) AND N4(q) = null (i.e. no pixels in V)} 11/20/2018 Visual Perception, Image Formation, Math Concepts

Visual Perception, Image Formation, Math Concepts M-adjacency m-adjacent: 1. q is in the set N4(p), or 2. q is in the set ND(p) and {N4(p) AND N4(q) = null (i.e. no pixels in V)} X [1] 11/20/2018 Visual Perception, Image Formation, Math Concepts