Practical Assignment 1

Dealine: 01.04.2021

Please put your name here:
Name: .......

Foreword

Implementation of a Minimal Classification System

Each basic machine learning system in principle comprises 3 stages:

• Training where the entire ML models' parametra are estimated with help of training data (data + groundtruth).
• Testing where test data is classified, and
• Evaluation where the testing results are evaluated by comparison with the groundtruth.

In this exercise, you will build a minimal classification system by implementing these three tasks. To make this easier, you are provided with a basic machine learining framework so that you just have to fill in the missing core parts.

• Download and install CMake
• Download (, build) and install OpenCV library
• Fork the current repository
• Using CMake generate the solution for miniml for your favorite IDE (e.g. Microsoft Visual Studio or XCode)
• Check that you can build and run miniml
• Do the assignment
• Add new folder "renders" to repository and save there the resulting renders (i.e. resulting class maps)
• Submit assignment by making a pull request

The provided machine learning framework contains a number of useful C++ classes, which you will need for the practical exercises:

• OpenCV class Vec3b, which incorporates standard vector operations such as addition, subtraction, dot product, cross product, etc.
• In order to handle and save image data, an OpenCV class Mat is included that handles pixels of type Vec3b. Pixels are stored in BGR (Blue, Green, Red) format, where each color component ranges from 0 to 255. For example, black=(0, 0, 0), white=(255, 255, 255), red=(0, 0, 255). With function imwrite(String& fileName, Mat& img) image data is saved into file. The bmp, jpg, etc. file formats are supported. See main.cpp on how to use this class.
• A class CPDFHistogram is provided for handling all PDF relatied procedures: sequential build, probability estimation, etc. Internally PDFs are stored as one-dimensional histograms.
• Furthermore a class CBayes implements the naive Bayes Model for classification (that we have studied on the lectures). It has a method addFeatureVec for sequential estimation of the Bayes model parameters and method getNodePotentials for classifying the test data.

Problem 1

Feature Extraction (Points 10)

We will start with extracting features from the images into the feature vector. For sake of simplicity the features were already calculated and are stored in the 001_fv.jpg and 002_fv.jpg files as red, green and blue channels. In order to solve the first problem please fill the feature vectors in the Training and Testing procedures in main.cpp file. The feature vector is a single channel column-matrix. It has nFeatures columns and 1 row.

In order to check your implementation, the first feature vector of the 001_fv.jpg should be equal to [132, 12, 73]

Hint1: In order to access pixels of a gray-scaled image img you can use OpenCV method img.at<byte>(y, x), where x and y are coordinates of the pixel.

Hint 2: In order to access pixels of an RGB color image img, you can use OpenCV method img.at<Vec3b>(y, x) and to access the distingct color values: img.at<Vec3b>(y, x)[c], where c is the channel index from 0 to 2.

Problem 2

Class Prior Probability (Points 25)

In order to apply the Bayes model we need to estimate the prior probabilities and the likelihoods from the training data. In this exersise we will estimate the prior probabilities. For this purpose we will use class CPDFHistogram. This class is designed to store, estimate and represent PDFs via histograms. Please study its implementation in the provided framework.

In CBayes class the prior probability is declared via smart pointer std::shared_ptr<CPDFHistogram> m_pPrior;, please see how it is initialized in the class constructor. In method CBayes::addFeatureVec() implement estimation of the prior probability.

Hint: Test your implementation with the printPriorProbabilities() function: if your implementation is correct, the output will be: 17.2% 0.4% 59.5% 9.9% 13.0% 0.0%. Answer the question: Which class is not represented at the training image?

Problem 3

The Bayes Classifier (Points 50)

Now in the CBayes::addFeatureVec() method you have complete implementation for estimating the prior probabilities and the likelihoods: thus the training procedure is complete. In this exercise, please finish the impmentation of the Bayes classifier in the CBayes::getNodePotentials() method.

The resulting potentials should be stored in res variable, which is a one-column matrix. The values of the resulting node potentials are already initialized with the prior probabilities. Hence your task is to multiply these prior probabilities with the likelihoods for every class and every feature. The likelihoods are stored in the array m_vPDF. You can check in the CBayes::addFeatureVec() method how to access a histogram for specific feature and state. Use method isEstimated() of the class CPDFHistogram in order to detect states, for which no training samples were met during the training procedure. Set the potential for such classes to be equal to zero.

Problem 4

Decision Theory (Points 15)

Now, when both training and testing procedures are ready, we need to apply the decision theory in order to set proper label to every pixel of the testing image.

In the testing procedure in the main.cpp file we classify the testing image using its features stored in the 002_fv.jpg file. The potentials for every pixel are returned from classifier into the potentials variable. Find the largest potential in potentials variable and assign the corresponding class label to the classLabel variable. Test your implementation. If everything is correct you should obtain 79,1% of accuracy and the class-map as follows:

Submission

Please submit the assignment by making a pull request. Important : Please make sure that

• No extra files are submitted (except those, which were mentioned in the assignment)
• The changes were made only in those files where you were asked to write your code
• The Continiouse Integration system (appVeyor) can build the submitted code
• The resulting images are also submitted in the folder "renders"