1

Midterm review

2

Project deliverables

Oral presentation (10%): presentations will take place in the last week of classes (presentation schedule will be determined today by drawing lots)

CENG 421 presentations must last no longer than 15 minutes, followed by 5-10 minutes of questions.ELEC 536 presentations must last no longer than 20 minutes, followed by 5 minutes of questions.15-20 minutes will not be enough to hit every detail of your project-I am interested in seeing how selective you are in identifying what is important and how clearly you convey that.Active in-class participation (questions asked for other project presentations than yours) will be marked

3

Project deliverables

functional demo of code - 10%final project report – 10%

Due on Monday April 6Guidelines about the demo and the

report will be posted on the course website

4

Topics covered by the second midtermBinary shape analysis

Mathematical morphology 13.1, 13.2, 13.3Shape description

Contour-based 8.2Region-based 8.3

Pattern Recognition (9.1, 9.2 + scan G&W)Supervised classification Classification error; RiskUnsupervised classification

Minimum distance classifierBayes classifier

1 dimensionextensions to multiple dimensionsNaïve BayesMultivariate Normal Bayesian classifier

Evaluation of classifiers (notes)

5

Allowed materials

CalculatorTwo sided formula sheet

Should contain formulas only (no worded definitions allowed)One of the learning objectives for the Computer Vision course is mastering the basic computer vision terminology

6

Mathematical morphology

Mathematical morphology uses concepts from set theory to analyze geometrical structures in an image

Morphological operators are useful for:Shape preprocessing or postprocessing(erosion, dilation, opening, and closing)Binary template matching (the hit-miss operator)Creating image descriptions such as the convex hull and the skeleton of the image (the hit-miss operator)

7

Mathematical morphology midterm questions can be about:

How to define the main concepts in mathematical morphology and , if requested, to give examples supporting your definitions

Example: What is a structuring element? What is its role in mathematical morphology? Give an example of a morphological operation that achieves two different results when applied on the same image but using two different structuring elements.

How to design a morphological operator to accomplish a specific task

Example: design a morphological operator for the detection of corners in the image

How to identify the sequence of morphological operators applied to an image, given the input image and its corresponding output.

Example: see sample question posted on the course site

8

What is a structuring element?

A structuring element is a shape, used to probe or interact with a given image.It can also be defined as a set.Different results obtained by using the same operation (dilation) with different structuring elements

9

Design a morphological operator for corner detection

Hit or miss operator for detecting each type of corner:For right corners:

10

Shape description

Criteria for selecting shape descriptorsTwo main classes

Region-basedContour-based

For both types of descriptions, we have discussed simple heuristics, and also more structured frameworks (Fourier descriptors, moments)ELEC 536: We have also discussed two research papers on:

shape description for interpolationMotion representation

11

Shape description midterm questions can be about

WorkflowExample: given an image, what needs to be done before a shape description algorithm is applied?

Factors affecting shape descriptorsExample: explain how high or low image resolution affects shape descriptors, their discriminability, and their repeatability.Example: briefly describe how noise affects chain codes, as well as one solution for dealing with this problem

InvarianceExample: what is the purpose of a shape descriptor being invariant to rotation, translation, and scaling?When would a descriptor invariant to a projective transformation be employed?

12

Briefly describe how noise affects chain codes, as well as one solution for dealing with this problem

13

Shape description midterm questions can be about

DefinitionsExample: define the boundary chain (Freeman) code in 4- and 8-connectivity and its derivative. Draw a simple shape and write out its boundary chain codeExample: give two examples of boundary representations and briefly describe pros and cons for each.Example: give 2 examples of region representations along with some of their pros and cons.Example: name one shape representation that allows us to describe a shape using some key-points. Briefly explain how these key points are obtained.

14

Name one shape representation that allows us to describe a shape using some key-points. Briefly explain how these key points are obtained.

This is just one possible solution! Can you think about an alternative?

15

ELEC 536 Shape description

1 or 2 midterm questions for ELEC 536 will be from assigned readings

Jeong and Radke, Reslicing axially sampled 3D shapes using elliptic Fourier descriptors, Medical Image Analysis 2007.

Bobick and Davis, The recognition of human movement using temporal templates, IEEE Trans. on Pattern Analysis Machine Intelligence 2001.

Concentrate on the why’s and how’s.Example: Why did Bobick and Dqvis choose a moment-based shape representation for the description of their templates?How is shape interpolation implemented in Jeong and Radke?

16

Pattern Recognition

We grouped pattern recognition techniques into two main approaches: statistic and structural.We focused on statistical pattern recognition.Terminology (you should be very comfortable by now with the meaning of each term): classes, feature vectors, feature space, classifiers, discriminantfunctions, supervised and unsupervised classification, etc.

17

Pattern Recognition topics

Supervised classificationMinimum distance classifierBayes classifier (in 1 dimension, in N-dimensions, Naïve Bayes and multivariate distributions)Bag of Words for Naïve BayesDesign of Bayesian classifiers: loss tables, risk minimization

Unsupervised classificationK-means

Evaluation of performance: ROC analysis, precision and recall, confusion matrix

18

Pattern recognition midterm questions can be about

Numerical calculations:Computing discriminant functions for:

the minimum distance classifierthe Bayes classifier

Showing the convergence process for K-meansEvaluating the performance of classifiers

Key features of the classifiers that we have discussedExamples follow

19

20

21

Performance evaluation of classification systems

Suppose that you have developed a vision-based classifier which inspects the quality of baked pastry (overcooked versus acceptable) based on the average colour of each sampleYou evaluate the performance of your classifier against ground truth. The test database consists in 1000 images of pastry samples. A human expert analyses each of these images and concludes that, among the 1000 samples, 200 are overcookedThe vision-based classifier classifies 140 images as overcooked and the remainder of 860 as acceptable. Among the 140 images classified as overcooked, the human expert identified 120 as overcooked and 20 as acceptable.Compute the precision and recall for each of the two classes (i.e. four values)

22

Calculating the precision and recall from the confusion matrix

Example. Consider the confusion matrix of a OCR that produces the following output over a test document set

Calculate the precision and recall for class a.

23

Questions on key aspects of the discussed classifiers

Briefly explain the two steps of a classification system.What is a training set? How is it designed? What influences the size of a training set?Briefly describe the Naïve Bayes classifier for an N-dimensional feature space.Underwhich circumstances a 1D Bayes classifier can be generalized to the Naïve Bayesclassifier?