[시각 지능] 컨벌루션 (Convolution)

컨벌루션 (Convolution)

 

 

수학 (특히 기능 분석)에서 컨벌루션은 함수의 모양이 다른 하나에 의해 수정되는 방식을 나타낸다. 컨볼루션이라는 용어는 결과 함수와 계산 프로세스를 모두 나타낸다. 그것은 하나가 반전되고 이동된 후 두 함수의 곱의 적분으로 정의된다. 적분은 모든 shift 값에 대해 평가되어 컨볼루션 함수를 생성한다.

 

from tensorflow.keras.datasets import mnist
import matplotlib.pyplot as plt

# mnist data download
(x_train, y_train), (x_test, y_test) = mnist.load_data()

plt.imshow(x_train[0], cmap='gray') # 1번째 데이터 
plt.show()

 

필터 (커널) 정의

 

import numpy as np

horizontal_filter = np.array([[1., 1., 1.], 
                             [0., 0., 0.], 
                             [-1., -1., -1.]])

vertical_filter = np.array([[1., 0., -1.],
                           [1., 0., -1.],
                           [1., 0., -1.]])

sharpen_filter = np.array([[0., -1., 0.],
                           [-1., 5., -1.],
                           [0., -1., 0.]])

blur_filter = np.array([[0.11, 0.11, 0.11],
                        [0.11, 0.11, 0.11],
                        [0.11, 0.11, 0.11]])

edge_1_filter = np.array([[1., 0., -1.],
                           [0., 0., 0.],
                           [-1., 0., 1.]])

edge_2_filter = np.array([[0., -1., 0.],
                           [-1., 4., -1.],
                           [0., -1., 0.]])

edge_3_filter = np.array([[-1., -1., -1.],
                           [-1., 8., -1.],
                           [-1., -1., -1.]])

 

컨벌루션 연산 함수 정의

 

def conv2d_simple(input_image, filter, filter_size):
    original_image_size = input_image.shape[0]

    conv_output_size = int((original_image_size - 3)/1 + 1)

    filtered_image = np.zeros((conv_output_size, conv_output_size))

    for i in range(conv_output_size):
        for j in range(conv_output_size):
            # 컨볼루션 연산
            conv_result = input_image[i:(i + filter_size), j:(j + filter_size)] * filter
            conv_sum = np.sum(conv_result)

            if(conv_sum > 255):
                conv_sum = 255
                
            filtered_image[i, j] = conv_sum
      
    return filtered_image

 

수직 / 수평 필터

 

https://www.analyticsvidhya.com/blog/2018/12/guide-convolutional-neural-network-cnn/

vertical_filtered_image = conv2d_simple(x_train[0], vertical_filter, 3)
horizontal_filtered_image = conv2d_simple(x_train[0], horizontal_filter, 3)

plt.figure(figsize=(6,4))

plt.subplot(1, 2, 1)
plt.title('vertical')
plt.imshow(vertical_filtered_image, cmap='gray')

plt.subplot(1, 2, 2)
plt.title('horizontal')
plt.imshow(horizontal_filtered_image, cmap='gray')

plt.tight_layout()
plt.show()

 

blur / sharpen 필터

 

https://medium.com/skylar-salernos-tech-blog/image-convolution-filters-explained-c878f1056e78

blur_filtered_image = conv2d_simple(x_train[0], blur_filter, 3)
sharpen_filtered_image = conv2d_simple(x_train[0], sharpen_filter, 3)

plt.figure(figsize=(6,4))

plt.subplot(1, 2, 1)
plt.title('blur')
plt.imshow(blur_filtered_image,cmap='gray')

plt.subplot(1, 2, 2)
plt.title('sharpen')
plt.imshow(sharpen_filtered_image,cmap='gray')

plt.tight_layout()
plt.show()

 

edge 필터

 

edge_1_filtered_image = conv2d_simple(x_train[0], edge_1_filter, 3)
edge_2_filtered_image = conv2d_simple(x_train[0], edge_2_filter, 3)
edge_3_filtered_image = conv2d_simple(x_train[0], edge_3_filter, 3)

plt.figure(figsize=(8,8))

plt.subplot(1, 3, 1)
plt.title('edge1')
plt.imshow(edge_1_filtered_image,cmap='gray')

plt.subplot(1, 3, 2)
plt.title('edge2')
plt.imshow(edge_2_filtered_image,cmap='gray')

plt.subplot(1, 3, 3)
plt.title('edge3')
plt.imshow(edge_3_filtered_image,cmap='gray')

plt.tight_layout()
plt.show()

 

https://en.wikipedia.org/wiki/Convolution

Convolution - Wikipedia