Gradient and phase + equations.
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Simple edge detector algorithm.
- Low-pass filter for noise removal
- Gradient calculation (all 3 directions)
- Gradient thresholding
Describe Canny’s edge detector.
- Smoothing with a Gaussian filter
- Gradient computation (magnitude and phase)
- Quantize the gradient angles
- Non-maxima suppression (reduce edge thickness)
- Hysteresis thresholding (improves edge connection)
Describe the Hough transform + equations.
Parameter spaces:
- ab-plane
- sinusoidal curve (vertical lines)
Accumulation cells:
- few cells
- many cells
Counter for each cell:
- an high counter means high number of pixels associated to a line in the image
Definitions of the morphological operators.
Erosion and Dilation.
- Opening: erosion + dilation
- Closing: dilation + erosion
Definition of image segmentation.
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Otsu’s method for image segmentation.
A global thresholding method based on the histogram.
Finds the optimal threshold: – Maximizes inter-class variance – Minimize intra-class variance
see the algortihm on OneNote
Describe the Region Growing algorithm.
- Initialization: threshold the image to select the bright areas
- Erode each component until 1 point is left (seed points)
- Specify a predicate to grow the seeds
Describe the Watershed algorithm.
A grayscale image can be seen as a topographic surface.
Three types of points:
– Local minima
– Steps: points at which a drop of water would fall to a given minima
– Watershed lines: points at which a drop of water
could fall into two (or more) different minima
GOAL: find watershed lines
Describe segmentation by clustering.
- We represent each pixel with a feature vector
- Distance function to compare vectors
Describe the k-means for clustering segmentation.
- k clusters and their centers
- minimize the objective function
Describe a similar method to the k-means.
- Create a density function
2. Look for the modes of the density function
How to create a density function?
- Starting point: set of samples
- Desired output: density function (PDF)
- Simple approach: kernel density estimation (AKA Parzen window technique)
Define the kernel used for creating the density function and how to derive the density function.
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What is mean shift?
Tool for finding peaks in high-dimensional data distribution without computing the density function explicitly; estimate its gradient instead!
Mean shift is a steepest-ascend method.
Describe how mean shift works.
- Compute mean shift vector 𝒎(𝒙)
- Move the kernel window by 𝒎(𝒙)
- Stop when the gradient is close to 0
- Prune the mode by perturbation (Saddle points)
What is the Markov Random Field (MRF) model? + equation of the energy function.
Approach for segmentating an image seen as a per-pixel labelling task.
- Define a set of labels
- Define an energy function (similar to a cost function)
- Assign a label to each pixel in order to minimize the energy
MRF: describe the data term and smoothness terms.
Data term:
1. Select 𝑚 pixels in the image: one per label
2. Create m feature vectors 𝒙
3. Evaluate 𝐸data as the 𝐿2-norm from the actual
pixel and the reference of that class
Smoothness terms:
- Potts model: any discontinuity has a constant penalization
- Linear smoothness cost: penalization depends on the label distance
Belief propagation + analytical formulation.
Belief propagation can be used for improving MRF.
Define the active contour framework Snakes.
Framework for delineating an object outline from a possibly noisy 2D image.
A simple elastic snake is defined by a set of n points, the internal elastic energy term and the external edge-based energy term.
The goal is to moving points in order to minimize the total energy,
