Hough Transforms and the Frequency Domain Flashcards
What is template matching?
Take a straight line, and match it to all possible image positions and orientations
Compute a measure of fit to the edge data e.g. count how many edges are under each possible line
Incredibly computationally expensive
What is parameter space?
A line that lies in m,c space, also known as parameter space, is a line that follows the traditional format of y = mx + c
However, the catch is that you only know x and y, not m and c, thus, it lies in m,c space
What does a line in m,c space tell us?
All pixels which lie on a line in (x,y) space are represented by lines which all pass through a single point in (m,c) space
The point through which they all pass gives the values of m’ and c’ for the equation y = m’x+c’
What does a Hough transform do, and how does it work?
To detect lines, you transform each edge point into m,c space and look for places where lots of lines intersect.
1 - Quantise (m,c) space into a 2D array A for appropriate steps of m and c
2 - Initialise all elements of A(m, c) to 0
3 - For each pixel (Xi, Yi) which lies on some edge in the image, we add 1 to all elements of A(m, c) whose indices m and c satisfy Yi = mXi + c
4 - Search for elements of A(m, c) which have large values. Each one found corresponds to a line in the original image
What does the Hough transform supply that is both an advantage and a disadvantage?
It only supplies the parameters of the lines it detects
What is frequency domain processing in regards to smoothing, sharpening and band limiting?
Smoothing - low pass filtering - attenuate high frequency components
Sharpening - high pass filtering - attenuate low frequency components
Band limiting - set all components to 0 outside a given frequency range
What is a Simple Frequency Domain Process?
Set the origin of the power spectrum to 0, leave the rest unchanged - reduces average intensity of image to 0, and negative intensities have been set to 0 in the display
How do you filter in frequency domains?
Filtering using frequency domains - multiply power spectrum by a mask designed to change the weights of selected basis functions
Low pass filtering results in a huge spike, whereas high pass filtering is a huge dip
What is high-pass filtering within frequency domain processing?
Raw high-pass filters set origin, and so mean intensity to 0, making images dark. Add a small constant to the filter so the mean remains positive
What does amplitude and phase mean in regards to Frequency Domain Processing?
Amplitude - relative prominence of basis functions
Phase - relative displacement of basis functions
