EEE-6512_Exam3_Lecture17

What problem motivates variable thresholding

Non-uniform illumination

What is the basic idea of variable thresholding by image partitioning

Subdivide an image into nonoverlapping rectangles

Why are the rectangles in variable thresholding chosen to be small

So the illumination within each rectangle is approximately uniform

Why can partitioning an image help thresholding under non-uniform illumination

Each subimage may have a more locally uniform histogram and illumination pattern

What is the main weakness of applying one global threshold under non-uniform illumination

One threshold may not separate foreground and background well across the whole image

What local quantities are used in variable thresholding based on local image properties

The local mean mxy and local standard deviation sigma_xy

What is the local threshold formula when the background is nearly constant

Txy = a + b sigma_xy

In local thresholding using Txy when is g(x

y)=1,When f(x,y) is greater than Txy

In local thresholding using Txy when is g(x

y)=0,When f(x,y) is less than or equal to Txy

What does the lecture call the modified thresholding approach based on local parameters

A thresholding rule using a logical predicate Q

When is Q true in the modified local thresholding method

When f(x,y) is greater than a and f(x,y) is greater than b times mxy

What is g(x

y) in the modified local thresholding method when Q is true,1

What is g(x

y) in the modified local thresholding method when Q is false,0

What is the role of a in the modified local thresholding rule

It is a threshold term that f(x,y) must exceed

What is the role of b in the modified local thresholding rule

It scales the local mean mxy in the second condition

What values are shown in the example figure for local thresholding based on local properties

a = 30 and b = 1.5 and mxy = mG

When does variable thresholding using moving averages work well

When the objects are small relative to the image size

What application is variable thresholding using moving averages said to be useful for

Document processing

How is scanning typically carried out in moving-average thresholding

Line by line in a zigzag pattern

Why is zigzag scanning used in moving-average thresholding

To reduce illumination bias

What is mk+1 in moving-average thresholding

The moving average mean intensity at the new point in the scanning sequence

What does n represent in the moving-average formula

The number of points used in computing the average

How are image borders handled in the moving-average formula example

The border of the image is padded with n minus 1 zeros

In moving-average thresholding what is Txy

Txy = b mxy

In moving-average thresholding when is g(x

y)=1,When f(x,y) is greater than Txy

In moving-average thresholding when is g(x

y)=0,When f(x,y) is less than or equal to Txy

What values are shown in the document-processing example for moving-average thresholding

N = 20 and b = 0.5

What is region growing according to the lecture

Each pixel starts as a separate region and adjacent similar regions are successively merged

For grayscale region growing what two statistics are computed for a region

The mean mu and the variance sigma squared

How is the mean mu of a grayscale region defined

It is the average of the intensities of the pixels in the region

How is the variance sigma squared of a grayscale region defined

It is the average squared deviation of pixel intensities from the mean

How is the dissimilarity of a pixel q measured in region growing

By its distance from the mean relative to the standard deviation

What is the dissimilarity formula used for a pixel q in region growing

d(q; I, mu, sigma) = |I(q) - mu| / sigma

What does a larger dissimilarity value imply in region growing

The pixel is less similar to the region

What is the basic segmentation definition used in splitting and merging

The image I is the union of regions R1 through Rn and the regions do not overlap

What does Q(Ri) measure in splitting and merging

The homogeneity of region Ri

What must be true about the regions in the splitting and merging formulation

Every pixel must belong to exactly one region

How do merging algorithms begin

With each pixel as a separate region

When do merging algorithms combine regions

When adjacent regions are similar to each other

How do splitting algorithms begin

With the entire image as a single region

When do splitting algorithms split a region

When the region is found to be nonhomogeneous

What is the conceptual difference between merging and splitting

Merging starts from many small regions and combines them while splitting starts from one large region and divides it

What method of segmentation is introduced after splitting and merging

Clustering

How many clusters are assumed in the clustering formulation

K clusters C1 through CK

What is associated with each cluster in the clustering formulation

A mean m1 through mK

What quantity is minimized in clustering according to the lecture

The least-squares error D

How is the least-squares error D defined in clustering

As the sum over clusters of the squared distances between points in each cluster and that cluster mean

Out of all possible partitions into K clusters which one is chosen

The one that minimizes D

What is the main goal of K-means clustering

Partition data into K clusters by minimizing within-cluster least-squares error

What kind of data does the lecture say K-means forms clusters from

A set of n-dimensional vectors

What is Step 1 of the K-means clustering algorithm

Set the iteration count ic to 1

What is Step 2 of the K-means clustering algorithm

Choose randomly a set of K initial means

What is Step 3 of the K-means clustering algorithm

For each vector compute its distance to each mean and assign it to the cluster with the nearest mean

What is Step 4 of the K-means clustering algorithm

Increment the iteration count and update the means

What is Step 5 of the K-means clustering algorithm

Repeat assignment and update until the cluster memberships no longer change

What stopping condition is given for K-means

Stop when Ck at one iteration equals Ck at the next iteration for all k

What does the lecture say can vary in K-means variants

Initialization of means and stopping criteria and methods for choosing K

What is one challenge K-means variants try to address

Determining the right number of clusters K for a given image

What are the main advantages of K-means given in the lecture

It is simple and fast and converges to a local minimum of the error function

What are the main disadvantages of K-means given in the lecture

You must choose K and it is sensitive to initialization and only finds spherical clusters and is sensitive to outliers

Why is sensitivity to initialization a weakness of K-means

Different starting means can lead to different final solutions

Why is needing to pick K a weakness of K-means

The correct number of clusters may not be known beforehand

What kind of clusters does standard K-means tend to find

Spherical clusters

Why can outliers be a problem for K-means

They can influence the means and distort the clustering result

What higher-order distinction should you know between global and variable thresholding

Global thresholding uses one threshold for the whole image while variable thresholding adapts the threshold locally

What higher-order distinction should you know between local-property thresholding and moving-average thresholding

Local-property thresholding uses local statistics like mean and standard deviation while moving-average thresholding uses a scanning-based moving mean

What higher-order distinction should you know between region growing and splitting

Region growing merges from many small initial regions while splitting divides from one large initial region

What higher-order distinction should you know between region-based segmentation and K-means clustering

Region-based methods rely on spatial homogeneity and adjacency while K-means groups vectors into K clusters by minimizing least-squares error

What summary topics does the lecture emphasize at the end

Global and local and adaptive thresholding and region growing and splitting merging and segmentation by clustering using K-means