TAILIEUCHUNG - Lecture Digital image processing - Lecture 18: Image Enhancement

This chapter presents the following content: Frequency domain filters, ideal lowpass filters, butterworth highpass filters, gaussian highpass filters, the laplacian in the frequency domain, high boost filtering, homomorphic filtering. | Digital Image Processing CSC331 Image Enhancement 1 Summery of previous lecture First order derivatives using the gradient operator Shobel operator using first order derivatives What are Edges in image? Modeling intensity changes Steps of edge detection 2 Todays lecture Frequency domain Filters Ideal Lowpass Filters Butterworth Highpass Filters Gaussian Highpass Filters The Laplacian in the Frequency Domain High boost filtering Homomorphic Filtering 3 Background Any function that periodically repeats itself can be expressed as the sum of sines and/or cosines of different frequencies, each multiplied by a different coefficient (Fourier series). 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 weighting function (Fourier transform). Background The frequency domain refers to the plane of the two dimensional discrete Fourier transform of an image. The purpose of the Fourier transform is to represent a signal as a linear combination of sinusoidal signals of various frequencies. Introduction to the Fourier Transform and the Frequency Domain The one-dimensional Fourier transform and its inverse Fourier transform (continuous case) Inverse Fourier transform: The two-dimensional Fourier transform and its inverse Fourier transform (continuous case) Inverse Fourier transform: Introduction to the Fourier Transform and the Frequency Domain The one-dimensional Fourier transform and its inverse Fourier transform (discrete case) DTC Inverse Fourier transform: 8 Frequency Domain Methods Spatial Domain Frequency Domain 9 Major filter categories Typically, filters are classified by examining their properties in the frequency domain: (1) Low-pass (2) High-pass (3) Band-pass (4) Band-stop 10 Example Original signal Low-pass filtered High-pass filtered Band-pass filtered Band-stop filtered 11 Frequency Domain Methods 12 13 Low pass filter functions left hand side: frequency domain .

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