Smoothing a photo 

Applying a box filter with hard edges doesn't result in a smooth blur on the output photo.

To improve this, the filter can be made smoother around the edges. One of the popular such filters is a Gaussian filter. This is a non-linear filter which enhances the effect of the center pixel and gradually reduces the effects as the pixel gets farther from the center. Mathematically, a Gaussian function is given as:

where μ is mean and σ is variance. 

An example kernel matrix for this kind of filter in a two-dimensional discrete domain is given as follows:

This two-dimensional array is used in normalized form and effect of this filter also depends on its width by changing the kernel width has varying effects on the output as discussed in further section. Applying Gaussian kernel as filter removes high-frequency components which results in removing strong edges and hence a blurred photo:

While this filter performs better blurring than a box filter, the implementation is also quite simple with OpenCV:

def plot_cv_img(input_image, output_image): 
    """ 
    Converts an image from BGR to RGB and plots 
    """ 
    fig, ax = plt.subplots(nrows=1, ncols=2)
    
    ax[0].imshow(cv2.cvtColor(input_image, cv2.COLOR_BGR2RGB)) 
    ax[0].set_title('Input Image')
    ax[0].axis('off')
    
    ax[1].imshow(cv2.cvtColor(output_image, cv2.COLOR_BGR2RGB)) 
    ax[1].set_title('Gaussian Blurred')
    ax[1].axis('off')
    plt.show()
    

def main():
    # read an image 
    img = cv2.imread('../figures/flower.png')
    
    # apply gaussian blur,
    
    # kernel of size 5x5, 
    # change here for other sizes 
    kernel_size = (5,5)
    # sigma values are same in both direction 
    blur = cv2.GaussianBlur(img,(5,5),0)
    
    plot_cv_img(img, blur)

if __name__ == '__main__':
    main()