IMAGE PROCESSING FREQUENCY DOMAIN PROCESSING Editor by DR

IMAGE PROCESSING FREQUENCY DOMAIN PROCESSING Editor by DR. FERDA ERNAWAN Faculty of Computer Systems & Software Engineering ferda@ump. edu. my OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Today’s Lesson • Frequency Domain Processing – Basic steps in frequency domain – Low pass Filter (smoothing filters) • Ideal lowpass, Butterworth lowpass, Gaussian lowpass – High pass Filter (sharpening filters) • Ideal highpass, Butterworth highpass , Gaussian highpass • Learning Outcomes: – To understand frequency filter operation. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License. 2

Images taken from Gonzalez and Woods, 2016 Basic steps for filtering Frequency domain filtering OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

The Basics of Filtering Images taken from Gonzalez and Woods, 2016 1. Fourier Spectrum (a) Scanning electron microscopy of a damaged circuit (b) Fourier Spectrum OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

The Basics of Filtering 2. Frequency Domain Filtering Fundamentals Result of filtering the image OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

DFT OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 DFT The results of DFT can be visualised by showing the spectrum signals as depicted in below: DFT OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 DFT Scanning electron microscope image Fourier spectrum OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Fourier Transform Spectrum Images taken from Gonzalez and Woods, 2016 FT Spectrum (a) (b) (c) (d) Original Image Fourier Spectrum Centered Spectrum after log transformation Centered FT Spectrum (centered + log) OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 Fourier Transform Spectrum (a) Vertical rectangle image (b) The corresponding spectrum of vertical rectangle image (c) Diagonal rectangle image (d) The corresponding spectrum of diagonal rectangle image OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 Filter Function Low Pass Filter High Pass Filter OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

The Basic of Filtering 3. Steps for Filtering: OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

The Importance of Zero Padding Images taken from Gonzalez and Woods, 2016 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

The Importance of Zero Padding (a) An image, (b) Result of blurring without padding (c) Result of blurring with padding OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Smoothing can be done by reducing high frequency values. An image filtering can be given as: G(u, v) = H(u, v)F(u, v) where F(u, v) denotes as DFT function and H(u, v) represents filter function. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

ILF Ideal lowpass filter (ILF) is defined by: where D 0 >0 and D(u, v) denotes the distance between a point (u, v) and the frequency center. D(u, v) can be defined as: OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

ILF H(u, v)=1 (a) an ideal low-pass filter (b) Filter (c) Filter radial OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 ILF Example: Sample Image Fourier spectrum OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

ILF (b) (a) Representation of an ideal lowpass, radius 5 (b) Intensity profile OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 BLF Butterworth lowpass filter (BLF) of order n with cut-off frequency at distance D 0 is defined as: (a)Perspective plot of a BLF (b) Filter (c) Filter radial of order 1 through 4 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Images taken from Gonzalez and Woods, 2016 BLF Spatial representation of Butterworth lowpass filter of order 1, 2, 5, and 20 and the corresponding intensity OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

BLF Example: OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

BLF Original image BLPF n=2, D 0=15 BLPF n=2, D 0=80 Less ringing than ILPF due to smoother transition BLPF n=2, D 0=5 BLPF n=2, D 0=30 BLPF n=2, D 0=230 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

GLF • Gaussian lowpass filter (GLPF) can be defined as: (a) GLPF function (b) filter function (c) Filter radial OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

GLF Original image Gaussian D 0=15 Gaussian D 0=85 Less ringing than BLPF but also less smoothing Gaussian D 0=5 Gaussian D 0=30 Gaussian D 0=230 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Lowpass Filters Comparison ILPF D 0=15 BLPF n=2, D 0=15 Gaussian D 0=15 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Lowpass Filtering Examples Gaussian lowpass filter can be used to connect broken text from scanning image. Blurring can help reading broken characters OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Lowpass Filtering Examples • Lowpass filtering can be used for publishing industry and printing. and. “cosmetic” processing Image GLPF with Do=100 GLPF with Do=80 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Sharpening (Highpass filter) High frequency coefficients contribute significantly in edges and fine detail of images. Highpass filter is a reverse of lowpass filter: HPF(u, v) = 1 – LPF(u, v) D 0 represents a cut-off frequency and n denotes the order of Butterworth filter. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Ideal Highpass Filters • An ideal highpass filter is defined by: • D 0 denotes a cut off distance. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Ideal Highpass Filters Image Sharpening (Highpass filter) IHPF D 0 = 15 IHPF D 0 = 30 IHPF D 0 = 80 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Butterworth Highpass Filters • Butterworth highpass filter is defined as: • n represents the order and D 0 denotes a cut off distance. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Butterworth Highpass Filters Image Sharpening (Highpass filter) BHPF n=2, D 0 =15 BHPF n=2, D 0 =30 BHPF n=2, D 0 =80 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Gaussian Highpass Filters • Gaussian highpass filter is defined as: • D 0 represents a cut off distance. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Gaussian High-pass Filters Image Sharpening (Highpass filter) Gaussian HPF n=2, D 0 =15 Gaussian HPF n=2, D 0 =30 Gaussian HPF n=2, D 0 =80 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Gaussian High-pass Filters Image Sharpening (Highpass filter) Gaussian HPF n=2, D 0 =15 BHPF n=2, D 0 =15 Gaussian HPF n=2, D 0 =15 OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

Highpass filtering Examples Example: using high pass filtering and thresholding for image enhancement Highpass filtering Thresholding Image Sharpening (Highpass filter) (a) Thumb print (b) Result obtained from highpass filter (b) Thresholding result Images taken from US National Institute of standards OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.

References • R. C. Gonzalez and R. E. Woods, 2016. Digital Image Processing, Pearson Education India; Third edition. • A. K. Jain, 2015. Fundamentals of Digital Image Processing, Pearson Education India; First edition. • R. C. Gonzalez, R. E. Woods and S. L. Eddins, 2017. Digital Image Processing Using MATLAB. Mc. Graw Hill Education; 2 edition. • S. Jayaraman, T. Veerakumar, S. Esakkirajan, 2017. Digital Image Processing, Mc. Graw Hill Education; 1 edition. OER Digital Image Processing by Ferda Ernawan (editor) work is under licensed Creative Commons Attribution. Non. Commercial-No. Derivatives 4. 0 International License.