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## Image Processing IB Paper 8 – Part A

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**Image ProcessingIB Paper 8 – Part A**Ognjen Arandjelovićhttp://mi.eng.cam.ac.uk/~oa214/**Lecture Roadmap**Face geometry • Lecture 1: Geometric image transformations • Lecture 2: Colour and brightness enhancement • Lecture 3: Denoising and image filtering • Lecture 4: Cross-section through out-of-syllabustechniques**Filter Design – Matched Filters**Consider the convolution sum of a discrete signal with a particular filter: 228+ 480+482+ 241 + … When is the filter response maximal?**Filter Design – Matched Filters**The summation is the same as for vector dot product: The response is thus maximal when the two vectors are parallel i.e. when the filter matches the local patch it overlaps.**Filter Design – Intensity Discontinuities**Using the observation that maximal filter response is exhibited when the filter matches the overlapping signal, we can start designing more complex filters: Kernel with maximal response to intensity edges 0.5 0.0 -0.5**Filter Design – Intensity Discontinuities**Better yet, perform Gaussian smoothing to suppress noise first: Gaussian kernel Noise suppressing kernel with high response to intensity edges**+**Unsharp Masking Enhancement The main principle of unsharp masking is to extract high frequency information and add it onto the original image to enhance edges: image output HPF Original edge Enhanced**Laplacian of Gaussian (LoG) Filter**The Laplacian of Gaussian is an isotropic kernel that responds maximally to changes in the 2nd derivative: 1D Laplacian of Gaussian 2D LoG as a surface 2D LoG as an image 2D Laplacian of Gaussian:**Laplacian of Gaussian (LoG) Filter**The response of the 1D Laplacian of Gaussian filter to an edge: Signal (edge) LoG filter Filter output -**Unsharp Masking Enhancement**Unsharp mask filtering performs noise reduction and edge enhancement in one go, by combining a Gaussian LPF with a Laplacian of Gaussian kernel: + = Gaussian smoothing Convolution with –ve Laplacian of Gaussian Result**Unsharp Masking – Example**Consider the following synthetic example: Gaussian smoothed then corrupted with Gaussian noise**Unsharp Masking – Example**After unsharp masking: Gaussian smoothed then corrupted with Gaussian noise**Motivation – Toy Problem**The problem: produce output image with higher pixel value indicating higher level of belief that a roughly square polygon of edge 225 is centered at it: 225**Matched Filtering May Be?**Given the material covered in the previous lecture, you may be tempted to create a matched filter: 225**Matched Filtering May Be?**Here is the output of convolving the filter with the example image: A rather ugly looking result with too sharp discontinuities (i.e. low robustness to small deformations in shape, angle or thickness)**Distance Transform**Rather, compute the distance transformed image – each pixel value indicates the minimal distance of that pixel to the nearest edge in the original image: Distance transformed Original image**Result after Distance Transform**Consider now the result of convolving our matched filter with the distance transformed image: The result is far better looking!**Salt and Pepper Noise**Consider an image synthetically corrupted with salt and pepper noise: “Pepper”(dark) “Salt”(bright)**Salt and Pepper Noise**Here is the result of denoising attempt using a Gaussian low-pass filter:**Median Filter**Median filter replaces the old pixel value by the median of its neighbourhood: ± 3 pixel neighbourhood (sorted) 0 91 92 93 93 97 108 Original value Median**Median Filter – 1D Example**The result of applying the median filter (with neighbourhood of size 7) on the corrupted 1D signal:**Median Filter – 2D Example**The result of applying the median filter (mask size 3 х 3) on the synthetically corrupted image: Noise virtually entirely removed No edge smoothing**Filter Comparison**The advantages of the median filter are easily seen when considering the difference to the ground truth: Median filtering Gaussian denoising RMS difference: 15 (from 20) RMS difference: 5 (from 20)**An Example Problem**Consider an image of a car plate acquired by a speed control camera: The plate is entirely unreadable due to motion blur Is it possible to somehow enhance this image to the level that the plate number can be read off?**Image Formation Model**Assuming constant car velocity* the motion blur is caused by simple spatial averaging in the direction of apparent velocity. As before, this is equivalent to convolving the original, sharp image with a simple pulse function. * A reasonable assumption, given that the exposure is relatively short.**/**Recovery Algorithm Given an estimate of the car velocity and our image formation model suggests the following algorithm: Degradation model 2D Fourier Transform De-blurred result 2D Fourier Transform**The Result**Using the pulse width of 15 pixels produces the following de-blurred result: RE03 TGZ**What is Image Super-Resolution**Given one or more low-resolution (LR) images, produce an enhanced, high-resolution (HR) image. • Observation model: Noise “True” image Observed LR image Transformation (geometric, photometric…)**SR via Non-Uniform Interpolation**One of the simplest forms of super-resolution takes on the form of interpolation from non-aligned samples: Not quite the same**Example – 2x Sampling Frequency**Simple scaling Non-uniform interpolation