Presentation 2 Edge Detection

Edge Detection Techniques – An Overview Djemel Ziou, Salvatore Tabbone

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Overview of the Overview • • • •

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Edge Definition Image Intensity Changes Step Edges Edge Detection – Smoothing – Differentiation – Gradient Operator – Gradient and Scale – Labeling Detector Metrics Optimization Lines and Junctions Implementation Issues Future Work Crucial Points

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What is an Edge? Physical meaning: a discontinuity • • •

Photometric Geometric Physical

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What is an Edge? Physical meaning: a discontinuity • • •

Photometric Geometric Physical

An edge corresponds to a change in the Image intensity

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Image Intensity Changes Three types of image intensity variations:

Steps

Lines

Junctions

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Step Edges

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Edge Detection Input

Output

Two Types of Edge Detectors vis-à-vis computer vision: •Contextual •“Autonomous”

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Edge Detection Schemes • Smoothing – Reduce noise – Regularize the image differentiation

• Differentiation – Evaluate the derivatives of the image (step edges, etc)

• Labeling – Localize edges – Suppress false edges 8

Smoothing Tradeoff: Noise Reduction vs. Information Loss Scale: The parameter that regulates the compromise between edge conservation and noise elimination

Green’s Function

Gaussian Function 9

Differentiation Localize variations of the image’s gray levels. Differentiation operators include • Gradient • LaPlacian • Second-order directional derivatives

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Gradient Operator vector: Direction of the gradient: Length of the gradient: Less computationally intensive approximations of the modulus:

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Gradient and Scale

σ=1

σ=4

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Labeling Essentials: • Edge Localization • S-N Ratio Improvement (false edge suppression) False Edges: • “Noised edges” • “Phantom edges” Hysteresis algorithm to define a true edge: Two thresholds are used. The all points of the edge must be above the low plausibility threshold, and at least one point above the high plausibility threshold. 13

Detector Metrics and Evaluation • Object Recognition • Intra-detector comparisons • Human judges: very few image characteristics are visible to humans!

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Optimal Detectors • Define performance criteria • Design a filter which optimizes the above criteria Examples: Spatial frequency, good detection, good localization, etc. Problems: • Outputs integer locations! • Edge is defined as a single point 15

Line Edges and Junctions Line: Local extrema of gray level intensity Junction: An intersection of two linear step edges. Types include T,Y,L,X, etc.

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Implementation General implementation is non-trivial. Efficiency, differentiation, smoothing, sampling must be tailored to the application.

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Forward! • Generalized implementations. • More and better algorithms for line edge detection. • Contextual detectors. • Objective evaluation techniques for detectors

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Points • Most widespread technique is the differentiation-smoothing-labeling approach. • Differentiation and smoothing algorithms are highly bound • False edge detection and suppression is of high importance • Tradeoff between false edge suppression and retaining true edge information 19