Digital Image Processing COSC 6380/ PDF Free Download

Digital Image Processing COSC 6380/4393 Lecture 21 Nov 16 th, 2017 Pranav Mantini Ack: Shah. M

Image Processing Geometric Transformation Point Operations Filtering (spatial, Frequency) Input Restoration/ Reconstruction Color Image Processing... Semantic meaning Output

Edge Detection Edge Detection Identify pixels that represent edges in the image

Why detect edges 1. Visual system The importance of using edges is also supported by nature The visual systems of mammals contain cells with gradient-based Gabor-like response. Initial stages of mammalian vision systems involve detection of edges and local features 2. Computer vision algorithms for Object detection and recognition Object recognition, stereo, texture analysis, motion analysis, image enhancement, image compression

Edge Formation

Edge Detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded in the edges Source: D. Lowe

What is an Edge? Discontinuity of intensities in the image Edge models

Characterizing edges An edge is a place of rapid change in the image intensity function Slide Credit: James Hays

Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal

Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal Where is the edge?

Solution: smooth first

Derivative theorem of convolution Differentiation is convolution, and convolution is associative:

Derivative theorem of convolution

Tradeoff between smoothing and localization Smoothed derivative removes noise, but blurs edge. Also finds edges at different scales.

Derivative in Two-Dimensions Definition Approximation Convolution kernels

Image Derivatives

Edge Detection Goals

Edge Detection Goals 1. Good detection: Low false alarm rate and low false dismissal rate: maximize S/ N ratio 2. Good localization: Mark point closest to center of true edge: minimize distance between marked point and center 3. Uniqueness: Only one response to a single edge 4. Good property measurement: Orientation, contrast, etc.

1D Edge Detection An ideal edge is a step function 22

1D Edge Detection The first derivative of I (x) has a peak at the edge The second derivative of I (x) has a zero crossing at the edge 23

Edge Detectors First order derivative based Second order derivative based

Edge Detectors First order derivative based Prewit Sobel Second order derivative based Marr-Hildreth (Laplacian of Gaussian ) Canny (Gradient of Gaussian)

First order edge detectors 1. Compute derivatives In x and y directions 2. Find gradient magnitude 3. Threshold gradient magnitude

Prewit: Compute derivatives In x directions Image Average smoothing in Y direction 1 1 1 Smooth image Gradient in X direction 1 0 1 Edges in X 1 0 1 1 0 1 1 0 1

Prewit: Compute derivatives In x and y directions Image Image Average smoothing in Y direction 1 1 1 Average smoothing in X direction 1 1 1 Smooth image Smooth image Gradient in X direction 1 0 1 Gradient in Y direction 1 0 1 Edges in X 1 0 1 1 0 1 1 0 1 Edges in Y 1 1 1 0 0 0 1 1 1

Sobel : Compute derivatives In x and y directions Image Image Average smoothing in Y direction 1 2 1 Average smoothing in X direction 1 2 1 Smooth image Smooth image Gradient in X direction 1 0 1 Gradient in Y direction 1 0 1 Edges in X 1 0 1 2 0 2 1 0 1 Edges in Y 1 2 1 0 0 0 1 2 1

Sobel Edge Detector

Pros: 1. Quick and simple Prewitt and Sobel Cons: 1. Detection: sensitive to noise 2. Uniqueness: Multiple responses (dependent on smoothing) 3. Requires tuning to define threshold

Second Order Derivative Edge Detection Methods Marr Hildreth Edge Detector 1. Smooth image by Gaussian filter S 2. Apply second order derivative to S 2 S (Laplacian) 3. Find zero crossings Scan along each row, record an edge point at the location of zero-crossing. Repeat above step along each column

Marr Hildreth Edge Detector Gaussian smoothing Find Laplacian

Marr Hildreth Edge Detector Laplacian of Gaussian (LoG)

Finding Zero Crossings 1. Four cases of zero-crossings : {+,-} {+,0,-} {-,+} {-,0,+} 2. Slope of zero-crossing {a, -b} is a+b. 3. To mark an edge compute slope of zero-crossing Apply a threshold to slope

Example

Marr Hildreth Edge Detector 1. Apply LoG to the Image 2. Find zero-crossings from each row 3. Find slope of zero-crossings 4. Apply threshold to slope and mark edges

Quality of an Edge

Canny Edge Detector Criterion 1: Good Detection: The optimal detector must minimize the probability of false positives as well as false negatives. Criterion 2: Good Localization: The edges detected must be as close as possible to the true edges. Single Response Constraint: The detector must return one point only for each edge point.

Canny Edge Detector Steps 1. Smooth image with Gaussian filter

Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image

Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image 3. Find magnitude and orientation of gradient

Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image 3. Find magnitude and orientation of gradient 4. Apply Non-maximum Suppression

Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image 3. Find magnitude and orientation of gradient 4. Apply Non-maximum Suppression 5. Apply Hysteresis Threshold

Smoothing Canny Edge Detector First Two Steps Derivative

Canny Edge Detector Derivative of Gaussian

Canny Edge Detector First Two Steps

Canny Edge Detector Third Step Gradient magnitude and gradient direction

Example

Derivative of Gaussian filter

Compute Gradients (DoG)

Edge Direction Vs Gradient Direction Gradient is maximum in the direction perpendicular to the edge Edge direction Maximum gradient direction Edge

Get Orientation at Each Pixel Threshold at minimum level Get orientation theta = tan 1 gy/gx

Canny Edge Detector Fourth Step Non maximum suppression

Canny Edge Detector Non-Maximum Suppression Suppress the pixels in S which are not local maximum

Canny Edge Detector Non-Maximum Suppression

Canny Edge Detector Hysteresis Thresholding If the gradient at a pixel is above High, declare it as an edge pixel below Low, declare it as a non-edge-pixel between low and high Consider its neighbors iteratively then declare it an edge pixel if it is connected to an edge pixel directly or via pixels between low and high.

Connectedness Canny Edge Detector Hysteresis Thresholding

Canny Edge Detector Hysteresis Thresholding

Canny Edge Detector Hysteresis Thresholding Scan the image from left to right, topbottom.

Canny Edge Detector Hysteresis Thresholding Scan the image from left to right, topbottom. The gradient magnitude at a pixel is above a high threshold declare that as an edge point

Canny Edge Detector Hysteresis Thresholding Scan the image from left to right, topbottom. The gradient magnitude at a pixel is above a high threshold declare that as an edge point Then recursively consider the neighbors of this pixel. If the gradient magnitude is above the low threshold declare that as an edge pixel.

Canny Edge Detector Hysteresis Thresholding

Before Non-max Suppression Slide

Hysteresis thresholding Threshold at low/high levels to get weak/strong edge pixels Do connected components, starting from strong edge pixels

Final Canny Edges

Effect of σ (Gaussian kernel spread/size) The choice of σ depends on desired behavior large σ detects large scale edges small σ detects fine features

Digital Image Processing

1. Pin hole camera Image Acquisition

Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE

Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE 3. OPTICAL IMAGING GEOMETRY light source (point source) emitted rays image object sensing plate, emulsion, etc focal length lens reflected rays

Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE 3. OPTICAL IMAGING GEOMETRY 4. Image Sampling and Quantization

Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE 3. OPTICAL IMAGING GEOMETRY 4. Image Sampling and Quantization 5. Spatial and Intensity Resolution 6. Resampling

Digital Image Processing

BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM

BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING

BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS

BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS 4. BLOB COLORING

BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS 4. BLOB COLORING 5. BINARY MORPHOLOGY

BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS 4. BLOB COLORING 5. BINARY MORPHOLOGY 6. Binary image Compression

Digital Image Processing

Image Enhancement and Filtering 1. Linear Point operations

Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping

Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations

Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations 4. DFT

Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations 4. DFT 5. Spatial filtering

Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations 4. DFT 5. Spatial filtering 6. Convolution Theorem 7. Frequency Filtering

Digital Image Processing

1. Degradation model Image Restoration

Image Restoration 1. Degradation model 2. Modelling and estimating Noise

Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise

Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise 4. Mean and order statistic filters

Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise 4. Mean and order statistic filters 5. Model degradation functions

Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise 4. Mean and order statistic filters 5. Model degradation functions 6. Inverse filtering

Digital Image Processing

Color Image Processing 1. Color Fundamentals

Color Image Processing 1. Color Fundamentals 2. Color Models

Color Image Processing 1. Color Fundamentals 2. Color Models 3. Psuedo color image processing

Color Image Processing 1. Color Fundamentals 2. Color Models 3. Psuedo color image processing 4. Full color image processing

Digital Image Processing

1. Edge Formation Edge Detection

Edge Detection 1. Edge Formation 2. Characterizing edges

Edge Detection 1. Edge Formation 2. Characterizing edges 3. First order Derivatives 4. Second order derivatives 5. Canny edge detector

Digital Image Processing ~