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Python OpenCV - Bicubic Interpolation for Resizing Image

Last Updated : 03 Jan, 2023
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Image resizing is a crucial concept that wishes to augment or reduce the number of pixels in a picture. Applications of image resizing can occur under a wider form of scenarios: transliteration of the image, correcting for lens distortion, changing perspective, and rotating a picture. The results of resizing greatly vary looking on the kind of interpolation algorithm used.

Note: While applying interpolation algorithms, some information is certain to be lost as these are approximation algorithms. 

What is Interpolation?

Interpolation works by using known data to estimate values at unknown points. For example: if you wanted to understand the pixel intensity of a picture at a selected location within the grid (say coordinate (x, y), but only (x-1,y-1) and (x+1,y+1) are known, you'll estimate the value at (x, y) using linear interpolation. The greater the quantity of already known values, the higher would be the accuracy of the estimated pixel value.

Interpolation Algorithms

Different interpolation algorithms include the nearest neighbor, bilinear, bicubic, and others. Betting on their complexity, these use anywhere from 0 to 256 (or more) adjacent pixels when interpolating. The accuracy of those algorithms is increased significantly by increasing the number of neighboring pixels considered while evaluation of the new pixel value. Interpolation algorithms are predominantly used for resizing and distorting a high-resolution image to an occasional resolution image. There are various interpolation algorithms one of them is Bicubic Interpolation.

Bicubic Interpolation

In addition to going 2x2 neighborhood of known pixel values, Bicubic goes one step beyond bilinear by considering the closest 4x4 neighborhood of known pixels — for a complete of 16 pixels. The pixels that are closer to the one that's to be estimated are given higher weights as compared to those that are further away. Therefore, the farthest pixels have the smallest amount of weight. The results of Bicubic interpolation are far better as compared to NN or bilinear algorithms. This can be because a greater number of known pixel values are considered while estimating the desired value. Thus, making it one of all the foremost standard interpolation methods.

Implementing Bicubic Interpolation with Python

Importing the necessary modules: We import all dependencies like cv2 (OpenCV), NumPy, and math.

Python 
# Import modules
import cv2
import numpy as np
import math
import sys, time

Writing the Interpolation Kernel Function for Bicubic Interpolation: The interpolation kernel for bicubic is of the form:

Kernel equation

Here the value of coefficient a determines the performance of the kernel and it lies mostly between -0.5 to -0.75 for optimum performance.

Python 
# Interpolation kernel
def u(s, a):
  
    if (abs(s) >= 0) & (abs(s) <= 1):
        return (a+2)*(abs(s)**3)-(a+3)*(abs(s)**2)+1
      
    elif (abs(s) > 1) & (abs(s) <= 2):
        return a*(abs(s)**3)-(5*a)*(abs(s)**2)+(8*a)*abs(s)-4*a
    return 0

Adding padding to the input image: Define padding function to add borders to your image. OpenCV has various padding functions. When interpolations require padding the source, the boundary of the source image needs to be extended because it needs to have information such that it can compute the pixel values of all destination pixels that lie along the boundaries.

Python 
# Padding
def padding(img, H, W, C):
    zimg = np.zeros((H+4, W+4, C))
    zimg[2:H+2, 2:W+2, :C] = img
    
    # Pad the first/last two col and row
    zimg[2:H+2, 0:2, :C] = img[:, 0:1, :C]
    zimg[H+2:H+4, 2:W+2, :] = img[H-1:H, :, :]
    zimg[2:H+2, W+2:W+4, :] = img[:, W-1:W, :]
    zimg[0:2, 2:W+2, :C] = img[0:1, :, :C]
    
    # Pad the missing eight points
    zimg[0:2, 0:2, :C] = img[0, 0, :C]
    zimg[H+2:H+4, 0:2, :C] = img[H-1, 0, :C]
    zimg[H+2:H+4, W+2:W+4, :C] = img[H-1, W-1, :C]
    zimg[0:2, W+2:W+4, :C] = img[0, W-1, :C]
    
    return zimg

Writing the bicubic interpolation function: Define bicubic function and pass the image as an input. (You can vary the scaling factor as x2 or x4 based on the requirement.)

Python 
# Bicubic operation
def bicubic(img, ratio, a):

    # Get image size
    H, W, C = img.shape

    # Here H = Height, W = weight,
    # C = Number of channels if the
    # image is coloured.
    img = padding(img, H, W, C)

    # Create new image
    dH = math.floor(H*ratio)
    dW = math.floor(W*ratio)

    # Converting into matrix
    dst = np.zeros((dH, dW, 3))

    # np.zeroes generates a matrix
    # consisting only of zeroes
    # Here we initialize our answer
    # (dst) as zero

    h = 1/ratio

    print('Start bicubic interpolation')
    print('It will take a little while...')
    inc = 0

    for c in range(C):
        for j in range(dH):
            for i in range(dW):

                # Getting the coordinates of the
                # nearby values
                x, y = i * h + 2, j * h + 2

                x1 = 1 + x - math.floor(x)
                x2 = x - math.floor(x)
                x3 = math.floor(x) + 1 - x
                x4 = math.floor(x) + 2 - x

                y1 = 1 + y - math.floor(y)
                y2 = y - math.floor(y)
                y3 = math.floor(y) + 1 - y
                y4 = math.floor(y) + 2 - y

                # Considering all nearby 16 values
                mat_l = np.matrix([[u(x1, a), u(x2, a), u(x3, a), u(x4, a)]])
                mat_m = np.matrix([[img[int(y-y1), int(x-x1), c],
                                    img[int(y-y2), int(x-x1), c],
                                    img[int(y+y3), int(x-x1), c],
                                    img[int(y+y4), int(x-x1), c]],
                                   [img[int(y-y1), int(x-x2), c],
                                    img[int(y-y2), int(x-x2), c],
                                    img[int(y+y3), int(x-x2), c],
                                    img[int(y+y4), int(x-x2), c]],
                                   [img[int(y-y1), int(x+x3), c],
                                    img[int(y-y2), int(x+x3), c],
                                    img[int(y+y3), int(x+x3), c],
                                    img[int(y+y4), int(x+x3), c]],
                                   [img[int(y-y1), int(x+x4), c],
                                    img[int(y-y2), int(x+x4), c],
                                    img[int(y+y3), int(x+x4), c],
                                    img[int(y+y4), int(x+x4), c]]])
                mat_r = np.matrix(
                    [[u(y1, a)], [u(y2, a)], [u(y3, a)], [u(y4, a)]])
                
                # Here the dot function is used to get the dot 
                # product of 2 matrices
                dst[j, i, c] = np.dot(np.dot(mat_l, mat_m), mat_r)

    # If there is an error message, it
    # directly goes to stderr
    sys.stderr.write('\n')
    
    # Flushing the buffer
    sys.stderr.flush()
    return dst

Taking input from the user and passing the input to the bicubic function to generate the resized image: Passing the desired image to the bicubic function and saving the output as a separate file in the directory.

Python3 
# Read image
# You can put your input image over here 
# to run bicubic interpolation
# The read function of Open CV is used 
# for this task
img = cv2.imread('gfg.png')

# Scale factor
ratio = 2

# Coefficient
a = -1/2

# Passing the input image in the 
# bicubic function
dst = bicubic(img, ratio, a)  
print('Completed!')

# Saving the output image
cv2.imwrite('bicubic.png', dst) 
bicubicImg=cv2.imread('bicubic.png')

Compare the generated image with the input image: Use the shape() method to compare the height, width, and color mode of both images.

Python3 
# display shapes of both images
print('Original Image Shape:',img.shape)
print('Generated Bicubic Image Shape:',bicubicImg.shape)

Complete Code:

Input Image:

gfg.png
Python3 
# import modules
import cv2
import numpy as np
import math
import sys
import time


# Interpolation kernel
def u(s, a):
    if (abs(s) >= 0) & (abs(s) <= 1):
        return (a+2)*(abs(s)**3)-(a+3)*(abs(s)**2)+1
    elif (abs(s) > 1) & (abs(s) <= 2):
        return a*(abs(s)**3)-(5*a)*(abs(s)**2)+(8*a)*abs(s)-4*a
    return 0


# Padding
def padding(img, H, W, C):
    zimg = np.zeros((H+4, W+4, C))
    zimg[2:H+2, 2:W+2, :C] = img
    
    # Pad the first/last two col and row
    zimg[2:H+2, 0:2, :C] = img[:, 0:1, :C]
    zimg[H+2:H+4, 2:W+2, :] = img[H-1:H, :, :]
    zimg[2:H+2, W+2:W+4, :] = img[:, W-1:W, :]
    zimg[0:2, 2:W+2, :C] = img[0:1, :, :C]
    
    # Pad the missing eight points
    zimg[0:2, 0:2, :C] = img[0, 0, :C]
    zimg[H+2:H+4, 0:2, :C] = img[H-1, 0, :C]
    zimg[H+2:H+4, W+2:W+4, :C] = img[H-1, W-1, :C]
    zimg[0:2, W+2:W+4, :C] = img[0, W-1, :C]
    return zimg


# Bicubic operation
def bicubic(img, ratio, a):
  
    # Get image size
    H, W, C = img.shape
    
    # Here H = Height, W = weight,
    # C = Number of channels if the 
    # image is coloured.
    img = padding(img, H, W, C)
    
    # Create new image
    dH = math.floor(H*ratio)
    dW = math.floor(W*ratio)

    # Converting into matrix
    dst = np.zeros((dH, dW, 3))  
    # np.zeroes generates a matrix 
    # consisting only of zeroes
    # Here we initialize our answer 
    # (dst) as zero

    h = 1/ratio

    print('Start bicubic interpolation')
    print('It will take a little while...')
    inc = 0
    
    for c in range(C):
        for j in range(dH):
            for i in range(dW):
              
                # Getting the coordinates of the
                # nearby values
                x, y = i * h + 2, j * h + 2

                x1 = 1 + x - math.floor(x)
                x2 = x - math.floor(x)
                x3 = math.floor(x) + 1 - x
                x4 = math.floor(x) + 2 - x

                y1 = 1 + y - math.floor(y)
                y2 = y - math.floor(y)
                y3 = math.floor(y) + 1 - y
                y4 = math.floor(y) + 2 - y
                
                # Considering all nearby 16 values
                mat_l = np.matrix([[u(x1, a), u(x2, a), u(x3, a), u(x4, a)]])
                mat_m = np.matrix([[img[int(y-y1), int(x-x1), c],
                                    img[int(y-y2), int(x-x1), c],
                                    img[int(y+y3), int(x-x1), c],
                                    img[int(y+y4), int(x-x1), c]],
                                   [img[int(y-y1), int(x-x2), c],
                                    img[int(y-y2), int(x-x2), c],
                                    img[int(y+y3), int(x-x2), c],
                                    img[int(y+y4), int(x-x2), c]],
                                   [img[int(y-y1), int(x+x3), c],
                                    img[int(y-y2), int(x+x3), c],
                                    img[int(y+y3), int(x+x3), c],
                                    img[int(y+y4), int(x+x3), c]],
                                   [img[int(y-y1), int(x+x4), c],
                                    img[int(y-y2), int(x+x4), c],
                                    img[int(y+y3), int(x+x4), c],
                                    img[int(y+y4), int(x+x4), c]]])
                mat_r = np.matrix(
                    [[u(y1, a)], [u(y2, a)], [u(y3, a)], [u(y4, a)]])
                
                # Here the dot function is used to get 
                # the dot product of 2 matrices
                dst[j, i, c] = np.dot(np.dot(mat_l, mat_m), mat_r)

    # If there is an error message, it
    # directly goes to stderr
    sys.stderr.write('\n')
    
    # Flushing the buffer
    sys.stderr.flush()
    return dst


# Read image
# You can put your input image over 
# here to run bicubic interpolation
# The read function of Open CV is used
# for this task
img = cv2.imread('gfg.png')

# Scale factor
ratio = 2
# Coefficient
a = -1/2

# Passing the input image in the 
# bicubic function
dst = bicubic(img, ratio, a)
print('Completed!')

# Saving the output image
cv2.imwrite('bicubic.png', dst)
bicubicImg = cv2.imread('bicubic.png')

# display shapes of both images
print('Original Image Shape:', img.shape)
print('Generated Bicubic Image Shape:', bicubicImg.shape)

Output:

Output Image:

bicubic.png

Explanation: 

Thus, from the above code, we can see that the input image has been resized using bicubic interpolation technique. The image given below has been compressed for publishing reasons. You can run the above code to see the implementation of increasing the size of the image smoothly using bicubic interpolation. The unknown pixel values here are filled by considering the 16 nearest known values.


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Python OpenCV - Bicubic Interpolation for Resizing Image

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