COMP 9517 WK3
2021 T1
Image Processing Recap
Spatial domain, intensity transformations (on single pixels)
• Image thresholding
• Otsu’s method
• Balanced histogram thresholding • Multi-band thresholding
• Image negative • Log transform • Power-law
Image Processing Recap
Spatial domain, intensity transformations (on single pixels):
• Piecewise-linear transformation • Contrast stretching
• Gray-level slicing
• Bit-plane slicing
• Histogram processing
• Arithmetic/Logic Operations
Image Processing Recap
Spatial Filtering (on neighbourhoods)
• Smoothing Filters: averaging, Gaussian
• Order-statistics Filters: median, min, max
• Sharpening Filters • Gradient
• Laplacian
• Combining filters • Padding
Frequency Domain Techniques
Goal:
• to gain working knowledge of Fourier transformation and frequency domain for use in IP
• Focus on fundamentals and relevance to IP • Not signal processing expertise
A sum of sines
Frequency vs Spatial Domain
• Spatial domain
• The image plane itself
• Direct manipulation of pixels
• Changes in pixel position correspond to changes in the scene
• Frequency domain
• Fourier transform of an image
• Directly related to rate of changes in the image
• Changes in pixel position correspond to changes in the spatial frequency
Frequency Domain Overview
• Frequency in image
• High frequencies correspond to pixel values that change rapidly across the image • Low frequency components correspond to large scale features in the image
• Frequency in domain
• Defined by values of the Fourier transform and its frequency variables (u, v)
Frequency Domain Overview
• Frequency domain processing
Fourier Series
• Periodic function can be represented as a weighted sum of sines and cosines of different frequencies
• Even functions that are not periodic (but whose area under the curve is finite) can be expressed as the integral of sines and/or cosines multiplied by a weight function
Discrete Fourier Transform
Discrete Fourier Transform
2-D Discrete Fourier Transform
Frequency Domain Filtering
• Frequency is directly related to rate of change, so frequencies in the Fourier transform may be related to patterns of intensity variations in the image.
• Slowest varying frequency at u = v = 0 corresponds to average gray level of the image.
• Low frequencies correspond to slowly varying components in the image- for example, large areas of similar gray levels.
• Higher frequencies correspond to faster gray level changes such as edges, noise etc.
Procedure for Filtering in the Frequency Domain
Notch Filter
Exploiting the correspondence
• If filters in the spatial and frequency domains are of the same size, then filtering is more efficient computationally in frequency domain
• However, spatial filters tend to be smaller in size.
• Filtering is also more intuitive in frequency domain
• Then, take the inverse transform, and use the resulting filter as a guide to design smaller filters in the spatial domain.
Gaussian Filter
DoG Filter
Multiresolution Processing
• Small objects, low contrast benefit from high resolution
• Large objects, high contrast, can make do with lower resolution
• If both present at the same time, multiple resolutions may be useful
• Local statistics such as intensity averages can vary in different parts of an image
• Exploit this in multiresolution processing
Image Pyramids
Image Pyramids
Image Features
• Image features are essentially vectors that are a compact representation of images
• They represent important information shown in an image
• Intuitive examples of image features: • Blobs
• Edges
• Corners • Ridges • Circles • Ellipses • Lines •…
Image Features
• We need to represent images as feature vectors for further processing in a more efficient and robust way
• Example of further processing include: • Object detection
• Image segmentation
• Image classification
• Content-based image retrieval • Image stitching
• Object tracking
Properties of Features
• Why not just use pixels values directly? • Repeatability (robustness)
• Should be detectable at the same locations in different images despite changes in illumination and viewpoint
• Saliency (descriptiveness)
• Similar salient points in different images should have similar features
• Compactness (efficiency) • Fewer features
• Smaller features
General Framework
Feature Types
• Colour features
• Colour histogram • Colour moments
• Texture features
• Haralick texture features
• Local binary patterns (LBP)
• Scale-invariant feature transform (SIFT) • Texture feature encoding
• Shape features
• Basic shape features
• Shape context
• Histogram of oriented gradients (HOG)
Colour Features
Colour Histogram
Colour Moments