Pattern Recognition

Table of contents

Lab 1. Decoding of a noisy number
Lab 2. Risk minimization (interval loss function)
Lab 3. Risk minimization (l1 loss function)
Lab 4. Analysis of Nonbayesian Strategy
Lab 5. Efficient computation of a sum of a subarray in 1D, 2D, 3D
Lab 6. Divisibility sum of digits
Lab 7. Binocular stereo vision
Lab 8. Binary Clustering
Lab 9. Finding the separating circle

Tasks and mathematical solutions

solutions.pdf.
tasks.pdf;

The tasks document is the intellectual property of Valerii Krygin (definability) and is included in this repository with explicit permission.

Acknowledgements

We would like to express our sincere gratitude to the course instructor, Valerii Krygin (definability), for the tremendous effort, dedication, and passion invested in teaching 📚 this course. His commitment to delivering high-quality material and supporting students throughout the learning process has been truly invaluable.

This course laid the foundation for our understanding of Python programming 🐍 and the fundamentals of computer vision 👁️🖥️, opening the door to further growth in these fields.

We will always remember the sleepless nights 😵‍💫 it required- and even more so, the lasting value, skills, and mindset it has given us for the future 🚀.

Setup

To run these applications, you need to have Python3.12.

Clone repo.
Create virtual environment.
```
python3.12 -m venv .venv
```
Activate it
```
source .venv/bin/activate
```
Install requirements:
```
pip install -r requirements.txt
```

Lab 1 – Decoding of a noisy number

Description

The program converts a number to a noisy (Bernoulli noise) image and then decodes it. Bayesian strategy for a binary loss function is used.

Usage

$ python3 decode_number.py --help                       
usage: decode_number.py [-h] --number {0,1,2,3,4,5,6,7,8,9} [--number_height NUMBER_HEIGHT] [--number_width NUMBER_WIDTH] --noise_level NOISE_LEVEL
                           [--seed SEED]

Decode noisy image of a number

options:
  -h, --help            show this help message and exit
  --number {0,1,2,3,4,5,6,7,8,9}
                        Number to encode and decode
  --number_height NUMBER_HEIGHT
                        Height of the number image.
  --number_width NUMBER_WIDTH
                        Width of the number image.
  --noise_level NOISE_LEVEL
                        Probability of Bernoulli noise. (0.0 to 1.0)
  --seed SEED           Random seed for reproducibility

Examples

$ python3 decode_number.py --number 9 --noise_level 0.56
Time: 0.022138417001769994 sec
Decoded number: 9

Original image	Noisy image	Decoded number
		9

Lab 2 – Risk minimization (interval loss function)

Description

Bayesian strategy for interval loss function is used.

Usage

$ python3 heatmap_interval.py --help
usage: heatmap_interval.py [-h] --n N [--seed SEED]

Minimize the risk of the Bayesian strategy for interval loss function.

options:
  -h, --help   show this help message and exit
  --n N        Number probability values. [0, 250]
  --seed SEED  Random seed for reproducibility

Example

$ python3 heatmap_interval.py --n 10
Input heatmap:  [102. 179.  92.  14. 106.  71. 188.  20. 102. 121.]
Heatmap normalized:  [0.10251256 0.1798995  0.09246231 0.01407035 0.10653266 0.07135678
 0.18894473 0.0201005  0.10251256 0.12160804]
Result: 4

Lab 3 – Risk minimization (L1 loss function)

Description

Bayesian strategy for L1 loss function is used.

Usage

$ python3 heatmap_l1.py --help
usage: heatmap_l1.py [-h] --n N [--delta DELTA] [--seed SEED]

Minimize the risk of the Bayesian strategy for L1 loss function.

options:
  -h, --help     show this help message and exit
  --n N          Number probability values. [0, 250]
  --delta DELTA  Delta value for loss function.
  --seed SEED    Random seed for reproducibility

Example

$ python3 heatmap_l1.py --n 10 --delta 2
Input heatmap:  [102. 179.  92.  14. 106.  71. 188.  20. 102. 121.]
Heatmap normalized:  [0.10251256 0.1798995  0.09246231 0.01407035 0.10653266 0.07135678
 0.18894473 0.0201005  0.10251256 0.12160804]
Result: 8

Lab 4 – Analysis of Nonbayesian Strategy

Usage

$ python non_bayesian_strategy.py --help                                      
usage: non_bayesian_strategy.py [-h] --values VALUES [VALUES ...] [--seed SEED] [--samples SAMPLES]

Non-Bayesian strategy analysis.

options:
  -h, --help            show this help message and exit
  --values VALUES [VALUES ...]
  --seed SEED
  --samples SAMPLES

Example

$ python non_bayesian_strategy.py --values 0 1 2 3 4 --seed 123 --samples 5000
q_quadratic: 2.0
q_binary: 2.0
q_third: 2.0
R_binary: 0.7247191011235955
R_quadratic: 1.9803370786516852
Mean quadratic risk: 1.9026322450747408
Mean binary risk: 0.6531887423660443

R-binary	R-quadratic

Lab 5 – Efficient computation of a sum of a subarray in 1D, 2D, and 3D.

Usage

$ python subsum.py

Numpy Simple Sum of a Subarray. 1D	Fast Sum of a Subarray. 1D

Lab 6 – Divisibility sum of digits

Description

The program generates a number image and then apply noise and checks whether it is divisible by a given number.

Usage

$ python3 division_recognition.py --help                                             
usage: division_recognition.py [-h] --n_digits N_DIGITS [--divisor DIVISOR] --noise_level NOISE_LEVEL [--height_digit HEIGHT_DIGIT] [--width_digit WIDTH_DIGIT]
                               [--n_iter N_ITER] [--seed SEED]

Generate a number image.

options:
  -h, --help            show this help message and exit
  --n_digits N_DIGITS   Number of digits to generate.
  --divisor DIVISOR     Check division by.
  --noise_level NOISE_LEVEL
                        Bernoulli noise level. (0 to 1).
  --height_digit HEIGHT_DIGIT
                        Height of the digit image.
  --width_digit WIDTH_DIGIT
                        Width of the digit image.
  --n_iter N_ITER       Test multiple times.
  --seed SEED           Random seed for reproducibility

Example

$ python3 division_recognition.py --n_digits 5 --noise_level 0.4 --n_iter 5 --seed 50
100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:00<00:00, 4917.12it/s]
Number:  71241  Divided by 3:  True
Number:  86765  Divided by 3:  False
Number:  69853  Divided by 3:  False
Number:  49472  Divided by 3:  False
Number:  20640  Divided by 3:  True
Success divisions:  2/5
time :  0.018097166999723413 sec

Image	Noisy Image

Lab 7 – Binocular stereo vision

Usage

$ python3 stereo.py --help                                                              
usage: stereo.py [-h] --left LEFT --right RIGHT [--alpha ALPHA] [--maxd MAXD]

Stereo DP Algorithm.

options:
  -h, --help     show this help message and exit
  --left LEFT    Path to left image
  --right RIGHT  Path to right image
  --alpha ALPHA  Smoothness weight
  --maxd MAXD    Max disparity

Example

python3 stereo.py --left examples/im2.ppm --right examples/im5.ppm --alpha 10 --maxd 50

Left Image	Right Image	Disparity Map

Images: D. Scharstein and R. Szeliski. A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision, 47(1/2/3):7-42, April-June 2002.

Lab 8 – Binary Clustering

Description

EM algorithm implementation.

Usage

$ python3 em.py --help                                                      
usage: em.py [-h] [--first_cluster_digit FIRST_CLUSTER_DIGIT] [--second_cluster_digit SECOND_CLUSTER_DIGIT] [--n_iter N_ITER]

EM for MNIST Clusters.

options:
  -h, --help            show this help message and exit
  --first_cluster_digit FIRST_CLUSTER_DIGIT
  --second_cluster_digit SECOND_CLUSTER_DIGIT
  --n_iter N_ITER

Example

$ python3 em.py --first_cluster_digit 0 --second_cluster_digit 2 --n_iter 50
Fetching MNIST...
Training on 10000 samples...
100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 50/50 [00:00<00:00, 170.35it/s]
Training completed in 0.3000 seconds
Testing on 3893 samples...
Test set accuracy: 0.9604

Lab 9 – Finding the separating circle

Description

Modification of Perceptron Algorithm where hyperplane is a circle (modified scalar product).

Usage

$ python3 perceptron_circle.py --help
usage: perceptron_circle.py [-h] [--n N] [--seed SEED]

Perceptron Circle Fit.

options:
  -h, --help   show this help message and exit
  --n N        Number of points to generate.
  --seed SEED  Random seed for reproducibility.

Example

$ python3 perceptron_circle.py --n 300 --seed 31
Original:  a=0, b=8, r=9
Predicted: a=0.261, b=8.462, r=8.711

Authors

Maksym Shylo (maksymshylo)
Ruslan Khomenko (Ruslan3584)

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Pattern Recognition

Acknowledgements

Setup

Lab 1 – Decoding of a noisy number

Description

Usage

Examples

Lab 2 – Risk minimization (interval loss function)

Description

Usage

Example

Lab 3 – Risk minimization (L1 loss function)

Description

Usage

Example

Lab 4 – Analysis of Nonbayesian Strategy

Usage

Example

Lab 5 – Efficient computation of a sum of a subarray in 1D, 2D, and 3D.

Usage

Lab 6 – Divisibility sum of digits

Description

Usage

Example

Lab 7 – Binocular stereo vision

Usage

Example

Lab 8 – Binary Clustering

Description

Usage

Example

Lab 9 – Finding the separating circle

Description

Usage

Example

Authors