Lecture 2

Question 1

Labelling

Answer 1

• After detecting foreground regions, label them
• Find group of pixels that connect to each other -> connected component analysis

Question 2

Connectivity

Answer 2

• 2D
  o 4-connectivity: any two pixels that have an Euclidean distance D = 1
  o 8-connectivity: any two pixels that have an Euclidean distance D < 2
• 3D
  o 6-connectivity: any two pixels that have an Euclidean distance D = 1
  o 26-connectivity: any two pixels that have an Euclidean
  distance D < 2

Question 3

Connected Component Analysis

Answer 3

• Two pass blob colour algorithm
• Forward pass: labelling takes into account connections to already
  labelled pixels and keeps track of connections
• Keep track of connected region using connectivity table
• Backward pass: replace labels with lowest connected label
  o In the example on the right we thus get labels 1 and 3

Question 4

Region Growing Algorithm

Answer 4

• Start from seed point (coordinates in an image)
  o Has some intensity value
• Check neighbours of the seed point, given a connectivity measure
• If neighbour fulfils some criteria it is included in the segmentation
  o For example similar texture or intensity
  o Usually requires use of a (double) threshold
• Repeat previous steps for all neighbours included in the segmentation
  o Segmented region grows this way
• Iterate until no improvements are made

Question 5

Segmentation Performance

Answer 5

• Class detection can have 4 different results, assuming the foreground is the positive class and
  the background is the negative class
  o True positive (TP): foreground pixel labelled as foreground
  o True negative (TN): background pixel labelled as background
  o False positive (FP): background pixel labelled as foreground
  o False negative (FN): foreground pixel labelled as background
• Accuracy: (TP + TN) / (TP + TN + FP + FN)
  o Problematic because we often have extremely imbalanced classes
• Specificity: TN / (TN + FP)
• Sensitivity/recall: TP / (TP + FN)
• Dice coefficient: 2TP / (2TP + FP + FN)
• Jaccard measure: TP / (TP + FP + FN) = Intersection over Union (IoU)

Question 6

Classification

Answer 6

• First-order statistical texture analysis -> histogram,
  typically normalised
• Can extract six features, shown on the right
• Does not consider spatial relationship and
  correlation between pixels
  o Identical histograms can belong to different textures

Question 7

Local Binary Pattern

Answer 7

• Takes a centre pixel gc and P neighbours gp at a distance R
  o Now takes spatial relations into account for classification
• Can also use K-nearest neighbours
  o But need to normalise features

Question 8

Gabor filters

Answer 8

• Multiply Gaussian kernel with sinusoidal function
  o Can change frequency of sinusoidal function
  o Can change orientation of sine wave
  o Can change scale (sigma) of the Gaussian function
• Real and imaginary component representing orthogonal directions
• Can create a bank of filters by varying parameters of filters

Question 9

Classification Performance Metrics

Answer 9

• Each classified case gets a likelihood score
• Often use ROC curves for analysis
• Check all thresholds for classification
  o For each, calculate sensitivity and 1-sensitivity
  o Gives a point in a 2D space, make curve through all points
• Calculate Area Under the Curve (AUC) for ROC curves
  o Range [0,1]
  o Identity line (AUC = 0.5) indicates random chance
  o Also seen as the probability that the model ranks a random positive example more
  highly than a random negative sample

Question 10

Detection

Answer 10

• Answers question such as: are there any abnormal structures in this image?
• Feature based
  o Extract relevant features for every location
  o Combine them (e.g. machine learning)
  o Threshold result (post-processing)
• Classifier: trained by combining several features
  o After classification, each detection gets a likelihood value
  o Then perform threshold and post-processing
• Post-processing
  o Morphology to remove small areas
  o Discard detection that are too small/large
  ▪ Can be learned from training data
  o Use prior knowledge to discard highly unlikely detected features

Question 11

Template Matching

Answer 11

• When you need to find a known object in an image
  o Can build a matched filter for appearance of the object
  ▪ High responses when doing convolution with matched filter and image

Question 12

Detection Performance Metrics

Answer 12

• Need to define a hit criterion
  o If d < 2r -> hit the object
  o Ensures that we do not need an exact match
• Sensitivity/recall (R) = TP / (TP+FN)
• Precision (P) = TP / (FP+TP)
• F1-score = 2PR (P+R) -> Balance between precision and recall
• Since each detection has a likelihood value, we can threshold to select
  detections
  o Influences TP, FP,FN
• Free-response receiver operating characteristic (FROC)
  o Like ROC curves, but now sensitivity vs average
  number of false positives