Targil 2 Image enhancement and edge detection For

Targil 2 Image enhancement and edge detection. For both we will use image derivatives.

Image enhancement • Histogram enhancement (histogram equalization…) • Reducing noise (smoothing, median) • Sharpening • Emphasize the details • Make the edges stronger • Problem: we magnify the noise

Sharpening: Subtracting The Laplacian F(x) F’’(x) F(x)-F’’(x)

Reminder : Convolution image Kernel, Convolver For example: means that

Image derivatives (Convolve with [1 -1]) (Convolve with [1 -1]T) A better kernel: (Convolve with ½*[1 0 -1])

Image derivatives (cont’) Problem: the image is not continuous. A better approximation: • Locally approximate the image with a smooth surface. • Compute the derivatives of this surface. Popular kernels:

The second derivative Check that:

The Laplacian Equation: The matrix: Subtracting the Laplacian:

Sharpening Example

Edge Detection Why do we need it ? • A compact representation of the image • More robust to light changes. • Easier to follow (tracking and computations of camera motion) • Segmentation: usually, edges are located at transitions between objects • Used for texture analysis

Edge Detection Wide edge Noise • What are “edges” ? Texture • How to find the edges ? T-junction Transition between objects • How to compute the exact location of an edge ?

The gradient The vector of derivatives Edge Size Edge Direction Derivative in Direction

The gradient Original Gradient

Example: Derivatives Ix = Iy = * -1 0 1 =

Gradient Ix 2 + Iy 2 =

Edge Localization-Zero Crossing Where exactly is the edge ? f Zero crossing of f’’ ’’f Problem: f’’ is very noisy Smooth first !

A smoothing with a 2 D Gaussian (We usually use the binomial coefficients instead. ) 11 12 1 1 3 3 1 1 4 6 4 1

Canny Edge Detection • Computing the image derivatives Gx, Gy – Smoothing with a Gaussian. – Using simple derivative kernels. • Compute the edge direction: • Take only the local maxima in that direction (to get an edge with width 1) • Hysteresis: Edge linking with two thresholds • Q. : What will be the width of the Gaussian?

Original Example Canny