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Chapter 5 – Image Pre-processing

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## Chapter 5 – Image Pre-processing

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**5.1 Brightness Transformations**5.2 Geometric Transformations 5.3 Local Pre-processing 5.4 Image Restoration Chapter 5 – Image Pre-processing**Objectives of image pre-processing:**(a) Suppress image information that is not relevant to later work (b) Enhancing information that is useful for later analysis**Classes of Image Pre-processing Methods**(a) Brightness Transformations (b) Geometric transformations 5.1 Brightness Transformations Categorization: (1) Point processing, Neighborhood processing (2) Position invariant, Position variant (3) Image Enhancement, Image Restoration**Histogram**• Histogram Equalization– image enhancement, position variant, point processing**Contrast Stretching**Transform function**Theorem: Let T be a differentiable strictly increasing**or strictly decreasing function. Letr be a random variable having density Let having density or Then,**Let transform function be**Then Called equalizationorlinearization. Discrete case: Let , , Transformation: 5-7**Specified Histogram Equalization**-- Specify the shape of the histogram that we wish the processed image to have. Histogram equalization Histogram specification Input image 5-12**Let**: gray levels of the input image I : gray levels of the output image O : the probability density function of r thatcanbe estimated from I : the given specified probability density function of z that we wish O to have Let and Then and Both are known 5-14**Procedure:**Given: input image (I), specification ( ) 1. Compute from I 2. Compute from 3. Compute from 4. Compute 5. Transform I into O by 5-15**Discrete case:**5-16**5.2. Geometric Transformations**Distorted grid image Scene grid Recovered grid image A geometric transform is a vector function T defined by Two steps: i) Pixel coordinate transformation ii) Brightness interpolation Applications: Remotely sensed image registration Bird-view generation Document skew 5-17**5.2.1. Pixel Coordinate Transformations**Geometric distortion types : a. variable distance, b. panoramic c. skew, e. scale, f. perspective Transformation model: where 5-19**Polynomial transformation:**Bilinear transformation: Affine transformation: Rotation: Scale change: Skewing : 5-20**Example:**Bilinear transform Needs at least 4 pairs of corresponding points to determine the parameters 5-21**Image Registration:**Steps: 1. Detect salient points of images 2. Determine the point correspondences between the two images 3. Compute the parameters of the transformation functions 5-23**(a)Nearest-Neighbor Interpolation**(b) Linear Interpolation 5-25**◎ Generalization○ Interpolation functionR**○ Examples: 5-27**○Substituting into**NN-interpolation 5-28**○Substituting into**linear interpolation 5-29**○ Bi-cubic Interpolation**-- Apply cubic interpolation first along the rows and then down the columns 5-31**5.3 Local (Neighborhood) Pre-Processing**-- Applies a function to a neighborhood of each pixel -- Different functions different objectives e.g., noise removal (smoothing), edge detection, corner detection 5-32**Neighborhood (window, mask)**Function+ Window = Filter 5-33**Filtration**(Filtering) Convolution: 5-34**5.3.1 Image Smoothing**Objective: noise removal • Linear Smoothing Filters 1-D case: Input data Mean filter Smoothed data 2-D case:**Gaussian Smoothing**1D: 2D: Discrete case:**Separable Filters**Convolution: e.g., Laplacian filter n × n filter: 2 (n × 1)filters: 5-38**Non-linear Smoothing Filters**。 K-nearest neighbors (K-NN) mean filter 。 Alpha-trimmed mean filter i) Order elements, ii) Trim off end elements iii) Take mean 。 Smoothing by a rotating masker**Dispersion**5-40**。 Mean Filters**(i) Arithmetic mean: (ii) Geometric mean: (iii) Harmonic mean: 5-41**(iv) Contra-harmonic mean:**。 Median filter 5-42**5.3.2 Edge Detectors**-- Edges are important information for image understanding Origin of edges Line drawing**Typical edge profiles:**Step edge (jump edge) Ramp edge Roof edge (crease edge) Smooth edge Line**2D case:**Gradient Magnitude Direction**。 Prewitt filters**Consider Horizontal filter: , Smooth filter: Combine Vertical filter: , Smooth filter: Combine**Input**Horizontal Vertical Edge image Binary image Thinning