CV Chapter 2 Image Processing Basics
Questions about the lecture 'Computer Vision' of the RWTH Aachen Chapter 2 Image Processing Basics
Questions about the lecture 'Computer Vision' of the RWTH Aachen Chapter 2 Image Processing Basics
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Cartes-fiches
What is the basic assumption of noise?
Noise is independent and identically distributed (iid)
What is the definition of salt&pepper noise?
Random occurrences of white and black pixels
What is the definition of impulse noise?
Random occurrences of white pixels
What is the definition of Gaussian noise? [2]
1. Variations in intensity drawn from a gaussian distribution
2. f(x,y) = f’(x,y) + peta(x,y) with peta ~ N(mye,sigma)
What is the MATLAB code for adding Gaussian noise? [2]
1. >> noise = randn(size(im)).*sigma;
2. >> output = im + noise;
What are the properties for filters? [6]
1. Shift invariant
2. Linear system
3. Commutative
4. Associative
5. Identity
6. Differentiation
What is the definition of shift invariant?
Operator depends on pattern not on position
What is the definition of linear system? [2]
1. Superposition with h*(f+g)=h*f+h*g
2. Scaling with h*f(x)=f(h*x)
What is the definition of commutative?
a*b=b*a
What is the definition of associative?
(a*b)*c=a*(b*c)
What is the definition of identity?
f*e=f
What is the definition of differentiation?
delta/deltaX (a*b) = deltaA/deltaX * b
What is the definition of correlation? [4]
1. Is first attempt
2. Replace each pixel by an average of neighbors
3. Window size of 2k+12 // Kernel or mask
4. G(i,j) = 1/(2k+1)² * Sumu=-kk Sumv=-kk F(i+u,j+v)// uniform weights
What is the definition of cross-correlation?
G(i,j) = Sumu=-kk Sumv=-kk H(u,v)*F(i+u,j+v) // With non-unfiorm weights and written as G=HxF
What is the definition of convolution?
G(i,j) = Sumu=-kk Sumv=-kk H(u,v)*F(i-u,j-v) // With non-unfiorm weights and written as G=H*F
What holds for cross-correlation and convolution?
Cross-correlation is convolution iff H(u,v) is H(-u,-v)
What is the definition of Gaussian filter? [4]
1. Gsigma = 1/(2pi*sigma²) * e-(x²+y²/2sigma²) // Fuzzy blob
2. Rotation invariant
3. Small/high sigma yields pointed/flat distribution // Size of kernel to 6*sigma
4. Implementation with first x and then y 1D filter with g(p) = 1/sqrt(2pi*sigma) * e-t²/2*sigma²
Which further filters exist? [5]
1. Sharpening [Not just difference?]
2. High-pass filter
3. High frequency emphasis
4. Histogram equalization
5. Median
What is the definition of median? [3]
1. Non-linear
2. Replace each pixel by the median of its neighbors // No new pixels
3. Edge preserving and removes spikes // Good for salt&pepper and impulse noise
What boundary types exist for filters? [3]
1. Full is the sum of F and H
2. Same is the size of F
3. Valid is the difference of F and H
Which behaviors near image boundary exist? [4]
1. Clip filter >> imfilter(f,g,0)
2. Wrap around >> imfilter(f,g,’circular’)
3. Copy edge >> imfilter(f,g,’replicate’)
4. Reflect across edge >> imfilter(f,g,’symmetric’)
What are the analogies to Fourier? [4]
1. Transforms of important functions possible
2. Duality means the better a function is localized somewhere, the worse it is localized elsewhere
3. Convolving in image domain is taking product in frequency domain
4. Filter attenuates or enhances specific frequencies
What is the motivation of multi-scale representation?
For fast search across scales
What are first approaches for re-sampling? [2]
1. Direct re-sampling misses information
2. Smoothing before re-sampling avoids artifacts but losses high frequencies
What is the Nyquist theorem?
“To recover frequency f, sample with at least 2f.”
What is the definition of the Gaussian image pyramid? [2]
1. Blur the original version and then re-sample with Gi+1 = blur(Gi) downscale by 2
2. Do not store blurred images at full resolution
What is the definition of the Laplacian image pyramid?
Difference the original and the re-sampled version with Li = Gi- expand(Gi+1) // Is a difference of gaussian (DoG) // No derivatives needed
What are the characteristics of filters as template matching? [2]
1. Filter looks like effects they are intended to find
2. Filter can be seen as set of dot products of image and some vector: a*b = |a||b|cos theta → theta = cos^-1(a*b/|a||b|) with theta the similarity
Which derivative objects are used for edge detections? [4]
1. Partial derivative with finite difference
2. Assorted finite difference filters
3. Image gradient G
4. Laplacian operator G²
What is the definition of the partial derivative?
df(x,y)dx = lim_e→0 f(x+e,y)-f(x,y)/e
What does hold for partial derivative with finite difference?
With e=1 is equivalent to convolution (1,-1)
Which assorted finite difference filters exist? [3]
1. Prewitt 2. Sobel and 3. Roberts
What is the definition of the prewitt filter?
Mz = Rows(-1,0,1) and My = rotLeft(Mz,90°)
What is the definition of the sobel filter?
Mx = (-1,0,1;-2,0,2;-1,0,1) and My = rotLeft(Mx,90°)
What is the definition of the roberts filter?
Mx = (0,1;-1,0) and My = rotLeft(Mx,90°)
What is the MATLAB code for assorted finite difference filters? [4]
>> My = fspecial(‘sobel’);
>> outim = imfilter(double(im), My);
>> imagesc(outim);
>> colormap gray;
What are the characteristics of image gradient G? [4]
1. Gf = [df/dx, df/dy]
2. Points in direction of most rapid intensity change
3. Direction theta = tan^-1 (df/dy / df/dx)
4. Edge strength ||Gf|| = \sqrt(df/dx² + df/dy²)
What is the definition of the laplacian operator G²?
G²f = d²f/dx² + d²f/dy²
How can we deal with noise regarding edge detection? [3]
1. Extract with smoothing
2. Maxima of differential d(h*f)/dx = dh/dx * f
3. Zero crossing of d²h/dx² * f with laplacian of gaussian (LoG)
What is the definition of edge detection?
Map 2D array of pixels to set of curves via post-processing gradients
