Digital Image Fundamentals 2.1.3 Bright adaptation and Discrimination The range of light intensity level to the human system: from the scotopic threshold to glare limit Brightness adaptation-the total range of distinct intensity level it can discriminate is small when compared with the total adaptation range Subjective brightness: is a logarithmic function of the light intensity incident on the eye Brightness adaptation level: the current sensitivity level of the visual system (Ba) The range of subjective brightness that the eye can perceive when adapted to this level (Bb) A level at and below (Bb)-indistinguishable black
Chapter 2: Digital Image Fundamentals
Experiment of Weber Ratio Chapter 2: Digital Image Fundamentals Experiment of Weber Ratio Good brightness discrimination
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals Mach band: a brightness pattern that is strongly scalloped, especially near the boundary (Fig. 2.7(b)) Simultaneous contrast: a region’s perceived brightness does not simply depend on its intensity (Fig. 2.8)
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals Optical illusion—eye fills in nonexisting information or wrongly perceive geometrical properties of objects
Chapter 2: Digital Image Fundamentals
2.3 Image sensing and acquisition Acquisition using a single sensor Microdensitometer A laser source coincident with the sensor Acquisition using a sensor strips Imaging acquisition using in-line sensors Computerized axial tomography Imaging acquisition using array sensors Electromagnetic and ultrasonic sensing devices CCD sensors - charge-coupled device A simple image formation model 2-D Image function : f(x,y) May be characterized by : amount of source illumination incident on the scene and amount of illumination reflected by the objects: f(x,y)= I(x,y) r(x,y)
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
2.4 Image sampling and quantization Convert the continuous sensed data to digital form Sampling Spatial transform: spatial coordinates(discrete locations) Quantization Amplitude transform: gray levels are converted to discrete values The quality of a digital image is determined to a large degree by the number of samples and discrete gray levels
Chapter 2: Digital Image Fundamentals
2.4.2 Representing digital images The complete MN digital image in the matrix form: f(x,y) Pixel, picture element A digital image use a traditional matrix A The number of gray levels L= 2k The dynamic range of an image : the range of values spanned by the gray scale High contrast image : an image whose gray levels span a significant portion of the gray scale as having a high dynamic range The number, b, of bits required to store a digitized image is b=M N K
Chapter 2: Digital Image Fundamentals
2.4.3 Spatial and gray-level resolution Sampling is the principal factor determining the spatial resolution Gray-level resolution: the smallest قابل للإدراك discernible range in gray level is the power of 2 due to hardware considerations The most common number: 8 bits Spatial resolution Sub-sampling Resampling Keep the number of samples constant and reduce the number of gray levels Reduce the number of bits while keeping the spatial constant Vary N and k simultaneously ISO reference curves If the number of bit are fixed, how to adjust the trade-off between spatial and gray-level resolution?
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
Chapter 2: Digital Image Fundamentals
2.4.4 Aliasing and Moire patterns frequency spectrum in terms of sines /cosines of various frequencies Band-limited functions the highest frequency is finite and that the function is of unlimited duration The Shannon sampling theorem if the function is sampled at a rate equal to or greater than twice its samples Under-sampled aliasing corrupts the sampled image Additional frequency component are introduced into the sampled function (aliased frequencies) Sampling rate is the number of samples taken per unit distance It is impossible to satisfy the sampling theorem Sol: work with sampled data that are finite in duration Gating function: convert a function of unlimited duration into a function of finite duration by multiplying a “ gating function”
Reducing the aliasing effect : reduce its high frequency by blurring the image Moirie patterns: a function of finite duration can be sampled over a finite interval without violating the sampling theorem Moirie patterns caused by a break up of the periodicity caused by interference between two sets of fine pattern grids, the scanner samples and the halftone screen in the original image
http://knight.fcu.edu.tw/~physics/MOVE/moire.html http://knight.fcu.edu.tw/~physics/MOVE/moire1.html http://knight.fcu.edu.tw/~physics/MOVE/moire2.html
2.4.5 zooming and shrinking digital images Two steps for zooming (1) the creation of new pixel locations (2) the assignment of gray levels to those new locations neighbor interpolation الزيادة : nearest neighborhood interpolation Pixel replication الإستنساخ Increase the size of an image an integer number of times a special case of nearest neighbor interpolation (Figs. 2.20(b) Defect: produces a checkerboard effect Bilinear interpolation Image shrinking Equivalent process of pixel location is row-column deletion:shrink by a non-integer factor Expand the grid to fit over the original image Do gray-level nearest neighbor or bilinear interpolation Shrink the grid to its original specified size Defect: Aliasing effect Sol: blur an image slightly
Chapter 2: Digital Image Fundamentals
2.5 Some basic relationship between pixels 2.5.1 Neighbor of a pixel Horizontal and vertical neighbors 4-neighbors of p 8-neighbors of p Four diagonal neighbors 2.5.2 Adjacency, connectivity, regions, and boundaries Connectivity of two pixels: if two pixels are connected, it must be determined If they are neighbors If their gray levels satisfy a specified criterion of similarity Three types of adjacency: 4-adjacency N4(V), 8-adjacency N8(V), m-adjacency(mixed adjacency) Digital path or curve Closed path 4-, 8-, or m-paths
Two pixels are said to be connected in S Boundary Connected component of S Connected set Boundary A region of the image R: R is a connected set The boundary of a region R: the set of pixels in the region that have one or more neighbors Edge 2.5.3 Distant measures Distant function or metric The Eulidean distance between p and q D4 (city block) distance : D8 (chessboard block) distance Dm distance: the shortest m-path between the points 2.5.4 Image operation on a pixel basis Operation is carried out between corresponding pixels 2.6 linear and nonlinear operations H(af+bg)= aH(f) + b H(g)
Euclidean distance De(p, q) = [(x - s)2 + (y - t)2 ]1/2 TheD4 distance (also called city-block distance) between p and q is defined as D4(p, q) = |x – s| + |y – t| TheD8 distance (also called chessboard distance) between p and q is defined as D8(p, q) = max (|x – s|, |y – t|)
(a) When V = {0, 1}, 4 path does not exist between p and q because it is impossible to get from p to q by traveling along points that are both 4adjacent and also have values from V . Figure P2.15(a) shows this condition it is not possible to get to q. The shortest 8path is shown in Fig. P2.15(b) its length is 4. In this case the length of shortest m- and 8paths is the same. Both of these shortest paths are unique in this case. (b) One possibility for the shortest 4path when V = (1, 2) is shown in Fig. P2.15(c) its length is 6. It is easily verified that another 4path of the same length exists between p and q. One possibility for the shortest 8path (it is not unique) is shown in Fig. P2.15(d) its length is 4. The length of a shortest mpath similarly is 4.