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Statistical Methods of Pattern Recognition

Laboratory work from the university course.

Setup

To run these applications you need to have Python3.10.

  1. Clone repo:
git clone https://github.com/maksymshylo/statistical-methods.git
  1. Create virtual environment.
python3.10 -m venv .venv
  1. Activate it
source .venv/bin/activate
  1. Install requirements:
pip install -r requirements.txt

Lab 1 - Recognition of a noised image.

Description

The program converts a string to noised image and then decodes it.

Usage

 $ python3 lab1/decode_string.py --help
usage: decode_string.py [-h] --input_string INPUT_STRING --noise_level NOISE_LEVEL [--seed SEED]

options:
  -h, --help            show this help message and exit
  --input_string INPUT_STRING
                        input string
  --noise_level NOISE_LEVEL
                        noise level of bernoulli distribution
  --seed SEED           seed to debug

Examples

python3 lab1/generate_string.py --input_string "billy herrington" --noise_level 0.35 --seed 45

Decoded string: "billy herrington"

Original image Noised image Decoded image 
python3 lab1/generate_string.py --input_string "van darkholme" --noise_level 0.45 --seed 45

Decoded string: "nde deauff sc"

Original image Noised image Decoded image

Lab 2 - Recognition of black vertical and horizontal lines

Description

The program creates an image with black vertical and horizontal lines, apply bernoulli noise, and denoise it.

Gibbs Sampling

Usage

$ python3 lab2/gibbs_sampler.py --help
usage: gibbs_sampler.py [-h] [--h H] [--w W] [--n_lines N_LINES]
                        [--noise_level NOISE_LEVEL]
                        [--column_prob COLUMN_PROB] [--n_iter N_ITER]

options:
  -h, --help            show this help message and exit
  --h H                 Height of image.
  --w W                 Width of image.
  --n_lines N_LINES     Number of horizontal and vertical lines.
  --noise_level NOISE_LEVEL
                        Noise level of bernoulli distribution.
  --column_prob COLUMN_PROB
                        Probability of column to be black.
  --n_iter N_ITER       Number of iterations for Gibbs Sampler.

Examples

 $ python3 lab2/gibbs_sampler.py --h 250 --w 250 --n_lines 40 --noise_level 0.42 --column_prob 0.5 --n_iter 100

column accuracy 99.6

row accuracy 99.6

Original image Noised image Decoded image
Precise solution

Usage

 $ python3 lab2/precise_solution.py --help
usage: precise_solution.py [-h] --h H --w W --n_lines N_LINES --noise_level NOISE_LEVEL --column_prob COLUMN_PROB

options:
  -h, --help            show this help message and exit
  --h H                 Height of image.
  --w W                 Width of image.
  --n_lines N_LINES     Number of horizontal and vertical lines.
  --noise_level NOISE_LEVEL
                        Noise level of bernoulli distribution.
  --column_prob COLUMN_PROB
                        Probability of column to be black.

Examples

 $ python3 lab2/precise_solution.py --h 250 --w 250 --n_lines 40 --noise_level 0.42 --column_prob 0.5

column accuracy 96.8

row accuracy 99.2

Original image Noised image Decoded image

Lab 3 - Gibbs Sampler for recognizing a noised string over another one

Note: Lengths of string should be the same.

Usage

 $ python3 lab3/row_over_row.py --help
usage: row_over_row.py [-h] --string_1 STRING_1 --string_2 STRING_2 --noise_level NOISE_LEVEL --n_iter N_ITER [--seed SEED]

options:
  -h, --help            show this help message and exit
  --string_1 STRING_1   The first string to decode.
  --string_2 STRING_2   The second string to decode.
  --noise_level NOISE_LEVEL
                        Noise level of bernoulli distribution.
  --n_iter N_ITER       Number of Gibbs Sampler iterations.
  --seed SEED           Seed to debug

Examples

python3 lab3/row_over_row.py --string_1 'deliver' --string_2 'reviled' --noise_level 0.3 --n_iter 10 --seed 67
Decoding strings...
Iteration 0. String 1: deliver; String 2: reviled.
Iteration 1. String 1: deliver; String 2: reviled.
Iteration 2. String 1: deliver; String 2: reviled.
Iteration 3. String 1: deliver; String 2: reviled.
Iteration 4. String 1: deliver; String 2: reviled.
Iteration 5. String 1: deliver; String 2: reviled.
Iteration 6. String 1: deliver; String 2: reviled.
Iteration 7. String 1: deliver; String 2: reviled.
Iteration 8. String 1: deliver; String 2: reviled.
Iteration 9. String 1: deliver; String 2: reviled.
Input string 1:  deliver
Input string 2:  reviled
The first decoded string:  deliver
The second decoded string:  reviled
Input string over string image Noised string over string image Decoded string 1 Decoded string 2 
 $ python3 lab3/row_over_row.py --string_1 'hello' --string_2 'world' --noise_level 0.35 --n_iter 25 --seed 67
Iteration 0. String 1: h|e|||||||||rdo||||; String 2: wo||||||||h||ld.
Iteration 1. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 2. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 3. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||||||||||||||||ld.
Iteration 4. String 1: h|||z|||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 5. String 1: he||||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 6. String 1: he||||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 7. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 8. String 1: he||||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 9. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 10. String 1: he||||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 11. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 12. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 13. String 1: he||||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 14. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||h||ld.
Iteration 15. String 1: h|e|||||||||r||||||||||||o||||; String 2: wo||||||||||||||||||||||ld.
Iteration 16. String 1: h||e||||||||r||||||||||||o||||; String 2: world.
Iteration 17. String 1: hello||||; String 2: world.
Iteration 18. String 1: hello||||; String 2: world.
Iteration 19. String 1: hello||||; String 2: world.
Iteration 20. String 1: hello||||; String 2: world.
Iteration 21. String 1: hello||||; String 2: world.
Iteration 22. String 1: hello||||; String 2: world.
Iteration 23. String 1: hello||||; String 2: world.
Iteration 24. String 1: hello||||; String 2: world.
Input string 1:  hello
Input string 2:  world
The first decoded string:  hello||||
The second decoded string:  world
Input string over string image Noised string over string image Decoded string 1 Decoded string 2

Some other examples of possible input strings with the same widths:

deliver <=> reviled
animal <=> lamina
depots <=> stoped
diaper <=> repaid
drawer <=> reward
looter <=> retool
murder <=> redrum
redips <=> spider
debut <=> tubed
deeps <=> speed
peels <=> sleep
serif <=> fires
steel <=> leets