Introduction to Image Processing with SciPy and NumPy

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Introduction to Image Processing with SciPy and NumPy Anil C R [email protected] Department of Electrical Engineering Indian Institute of Science

September 19, 2010

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Outline 1

Introduction Image Processing What are SciPy and NumPy?

2

Some Theory Filters The Fourier Transform

3

Doing the Stuff in Python

4

Demo(s)

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

Outline 1

Introduction Image Processing What are SciPy and NumPy?

2

Some Theory Filters The Fourier Transform

3

Doing the Stuff in Python

4

Demo(s)

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

What are Images? Continious domain, Continious range f : R2 → R(R3 ) Discrete domain, Continious range f : Z2 → R(R3 ) Discrete domain, Discrete range f : Z2 → Z(R3 ) Finite domain, Continious range f : Zm × Zn → R(R3 ) Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

What are Images? Continious domain, Continious range f : R2 → R(R3 ) Discrete domain, Continious range f : Z2 → R(R3 ) Discrete domain, Discrete range f : Z2 → Z(R3 ) Finite domain, Continious range f : Zm × Zn → R(R3 ) Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

Using Matrices to Represent Images f as an element of Rm×n (Rm×n×k ) ⇒ Linear Algebra ⇒ LAPACK, BLAS, etc ⇒ FORTRAN, C, etc ⇒ Super Hard ⇒ MATLAB ⇒ Super Expensive ⇒ SciPy + NumPy, GNU Octave, Scilab, etc PyCon 2010 ⇒ SciPy + NumPy Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

Outline 1

Introduction Image Processing What are SciPy and NumPy?

2

Some Theory Filters The Fourier Transform

3

Doing the Stuff in Python

4

Demo(s)

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

NumPy

Numerical Processing Started off as numecric written in 1995 by Jim Huguni et al. Numeric was slow for large arrays and was rewritten for large arrays as Numarray Travis Oliphant, in 2005 merged them both into NumPy

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Image Processing SciPy and NumPy

SciPy

Libraries for scientific computing Linear Algebra Statistics Signal and Image processing Optimization ODE Solvers

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Outline 1

Introduction Image Processing What are SciPy and NumPy?

2

Some Theory Filters The Fourier Transform

3

Doing the Stuff in Python

4

Demo(s)

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Filters

Keep what you want and throw away the rest Studying filters is the most important part in Image Processing Classified into linear and non-linear filters

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Linear Filters

Given images f1 , f2 , . . . , fn a filter H is called linear if H(α1 f1 + α2 f2 + · · · + αn fn ) = α1 H(f1 ) + α2 H(f2 ) + · · · + αn H(fn ) Linearity can be useful in fast computation

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Outline 1

Introduction Image Processing What are SciPy and NumPy?

2

Some Theory Filters The Fourier Transform

3

Doing the Stuff in Python

4

Demo(s)

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Time and Frequency Domains

⇓

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Fourier Transform

Continious FT F (ωx x, ωy y ) =

RR

R2

f (x, y )exp(−iωx x − iωy y )dxdy

Discrete FT F (ωx x, ωy y ) =

PM PN 0

0

x f (x, y )exp(−i{ 2πω M x −

Notation: F is the FT of f , also F = F{f }

Anil C R

Image Processing

2πωy N y })

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Convolution Continious (f ~ g)(x, y ) =

RR

R2

f (x 0 , y 0 )g(x − x 0 , y − y 0 )dxdy

Discrete PP 0 0 (f ~ g)(x, y ) = Z2 f (x, y )g(x − x , y − y ) Theorem (a) F{f ~ g} = FG (b) F{fg} = F ~ G Any linear filter can be written as a convolution. Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Filters The Fourier Transform

Fast Fourier Transform (FFT)

Computing the Discrete Fourier Transform takes O(n2 m2 ) for an m × n image FFT Computes the same in O(n log nm log m)

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Interactive Python

Install NumPy Install SciPy Install Matplotlib Install IPython Running IPython $ ipython -pylab

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Fast Fourier Transform (FFT)

FFT in NumPy In[1]: from scipy import lena In[2]: f = lena() In[3]: from numpy.fft import fft2 # unnecessary if you invoke ipython with -pylab In[4]: F = fft2(f) In[5]: imshow(real(F))

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Fast Fourier Transform (FFT)

FFT in NumPy In[1]: from scipy import lena In[2]: f = lena() In[3]: from numpy.fft import fft2 # unnecessary if you invoke ipython with -pylab In[4]: F = fft2(f) In[5]: imshow(real(F))

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Fast Fourier Transform (FFT)

FFT in NumPy In[1]: from scipy import lena In[2]: f = lena() In[3]: from numpy.fft import fft2 # unnecessary if you invoke ipython with -pylab In[4]: F = fft2(f) In[5]: imshow(real(F))

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Fast Fourier Transform (FFT)

FFT in NumPy In[1]: from scipy import lena In[2]: f = lena() In[3]: from numpy.fft import fft2 # unnecessary if you invoke ipython with -pylab In[4]: F = fft2(f) In[5]: imshow(real(F))

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Fast Fourier Transform (FFT)

FFT in NumPy In[1]: from scipy import lena In[2]: f = lena() In[3]: from numpy.fft import fft2 # unnecessary if you invoke ipython with -pylab In[4]: F = fft2(f) In[5]: imshow(real(F))

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells

Input Image Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells

Output Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure

Consider the image:

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure Cont’d

Find the variance of the neighborhood of each pixel, store them as a 2D array

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure Cont’d

Find the variance of the neighborhood of each pixel, store them as a 2D array

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure Cont’d

Find the variance of the neighborhood of each pixel, store them as a 2D array

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure Cont’d

Variance map (V ) V > E{V }

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure Cont’d

Variance map (V ) V > E{V }

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Demo: Cells Procedure Cont’d

Algorithm on the cell image:

Anil C R

Image Processing

Introduction Some Theory Doing the Stuff in Python Demo(s) Q and A

Q and A

Anil C R

Image Processing