Image Processing Class from Scratch on Python

Contents

• 1.1 What am I using?
• 1.2 What this blog includes?
• 2 Steps
  • Initializing a ImageProcessing class
  • Adding a read method
  • Adding a show method
  • Color conversion
  • Adding a convolution method
    • Recall the mathematics of Convolution Operation

Let’s write a Image Processing Codes from Python on Scratch What will you do when you suddenly think about Convolutional Neural Networks from Scratch while serving cows? For me, I wrote some codes for image processing before thinking about those codes. Once again I am not going to write another OpenCV here.

1.1 What am I using?

• Numpy for array operations
• imageio builtin library for reading image
• warnings to show warning
• matplotlib for visualizing

1.2 What this blog includes?

• Converting an image into Grayscale from RGB.
• Convolution of an image using different kernels.

2 Steps

• Initializing a ImageProcessing class.
• Adding a read method
• Adding a show method
• Adding color conversion method
• Adding a convolution method

Initializing a ImageProcessing class

class ImageProcessing:
    def __init__(self):
        self.readmode = {1 : "RGB", 0 : "Grayscale"} # this dictionary will hold readmode values

Adding a read method

    def read_image(self, location = "", mode = 1):
        """
            Uses imageio on back.
            location: Directory of image file.
            mode: Image readmode{1 : RGB, 0 : Grayscale}.
        """
        img = imageio.imread(location)
        if mode == 1:
            img = img
        elif mode == 0:
            img = 0.21 * img[:,:,0] + 0.72 * img[:,:,1] + 0.07 * img[:,:,2]
        elif mode == 2:
            pass
        else:
            raise ValueError(f"Read mode not understood. Choose from {self.readmode}.")
        return img

• This method only wraps the imageio, but I am applying a concept of RGB to GRAYSCALE conversion.
• By default, imageio reads in RGB format.
• A typical RGB to GRAYSCALE can be done on below concepts (taken from):-
  • Average Method: \begin{equation} Grayscale = \frac{R + G + B}{3} \end{equation} All channels are given a 33% contribution.
  • Weighted Method of luminosity method \begin{equation} Grayscale = 0.3R + 0.59G + 0.11*B \end{equation} Red channel have 30%, Green have 59 and Blue have 11% contribution.
    But I am using a different version of the method (taken from).
• If the user enters a different mode, then raise an error.

Adding a show method

def show(self, image, figsize=(5, 5)):
    """
        Uses Matplotlib.pyplot.
        image: An image to be shown.
        figsize: How big an image to show. From plt.figure()
    """
    fig = plt.figure(figsize=figsize)
    im = image
    plt.imshow(im, cmap='gray')
    plt.show()

Nothing to say here, docstring is enough.

Color conversion

    def convert_color(self, img, to=0):
        if to==0:
            return  0.21 * img[:,:,0] + 0.72 * img[:,:,1] + 0.07 * img[:,:,2]
        else:
            raise ValueError("Color conversion can not understood.")

I still have not thought about grayscale to RGB conversion. But even using OpenCV cv2.cvtColor(img, cv2.COLOR_GRAY2BGR), we can not get a complete BGR image.

Adding a convolution method

    def convolve(self, image, kernel = None, padding = "zero", stride=(1, 1), show=False, bias = 0):
        """
            image: An image to be convolved.
            kernel: A filter/window of odd shape for convolution. Used Sobel(3, 3) default.
            padding: Border operation. Available from zero, same, none.
            stride: How frequently do convolutions?
            show: whether to show result
            bias: a bias term(used on Convolutional NN)
        """
        if len(image.shape) > 3:
            raise ValueError("Only 2 and 3 channel image supported.")
        if type(kernel) == type(None):
            warnings.warn("No kernel provided, trying to apply Sobel(3, 3).")
            kernel = np.array([[1, 0, -1],
                              [1, 0, -1],
                              [1, 0, -1]])
            kernel += kernel.T
        kshape = kernel.shape
        if kshape[0] % 2 != 1 or kshape[1] % 2 != 1:
            raise ValueError("Please provide odd length of 2d kernel.")
        if type(stride) == int:
                 stride = (stride, stride)
        shape = image.shape
        if padding == "zero":
            zeros_h = np.zeros(shape[1]).reshape(-1, shape[1])
            zeros_v = np.zeros(shape[0]+2).reshape(shape[0]+2, -1)
            padded_img = np.vstack((zeros_h, image, zeros_h)) # add rows
            padded_img = np.hstack((zeros_v, padded_img, zeros_v)) # add cols
            image = padded_img
            shape = image.shape  
        elif padding == "same":
            h1 = image[0].reshape(-1, shape[1])
            h2 = image[-1].reshape(-1, shape[1])
            padded_img = np.vstack((h1, image, h2)) # add rows
            v1 = padded_img[:, 0].reshape(padded_img.shape[0], -1)
            v2 = padded_img[:, -1].reshape(padded_img.shape[0], -1)
            padded_img = np.hstack((v1, padded_img, v2)) # add cols
            image = padded_img
            shape = image.shape
        elif padding == None:
            pass
        rv = 0
        cimg = []
        for r in range(kshape[0], shape[0]+1, stride[0]):
            cv = 0
            for c in range(kshape[1], shape[1]+1, stride[1]):
                chunk = image[rv:r, cv:c]
                soma = (np.multiply(chunk, kernel)+bias).sum()
                try:
                    chunk = int(soma)
                except:
                    chunk = int(0)
                if chunk < 0:
                    chunk = 0
                if chunk > 255:
                    chunk = 255
                cimg.append(chunk)
                cv+=stride[1]
            rv+=stride[0]
        cimg = np.array(cimg, dtype=np.uint8).reshape(int(rv/stride[0]), int(cv/stride[1]))
        if show:
            print(f"Image convolved with \nKernel:{kernel}, \nPadding: {padding}, \nStride: {stride}")
        return cimg

What is happening above?

• First the kernel is checked, if not given, used from sobel 3 by 3
• If the given kernel shape is not odd, error is raised.
• For padding, numpy stack methods are used.
• Initialize an empty list to store convoluted values
• For convolution,
  • we loop through every rows in step of kernel’s row upto total img rows
  • loop through every cols in step of kernel’s col up to total img cols
  • get a current chunk of image and multiply its elements with the kernel’s elements
  • if current sum is greater than 255, set it 255
  • append sum to list
• Finally convert the list into an array then into the right shape.

Recall the mathematics of Convolution Operation

\begin{equation} g(x, y) = f(x,y) * h(x,y) \end{equation} Where f is an image function and h is a kernel or mask or filter.

What happens on convolution can be clear from the matrix form of operation. Lets take an image of 5X5 and a kernel of 3X3 sobel y.

\[\begin{equation*} f(x, y) = \begin{pmatrix} 1 & 10 & 11 & 20 & 30\\12 & 200 & 152 & 223 & 60 \\100 & 190 & 11 & 20 & 10\\102 & 207 & 102 & 223 & 50 \\18 & 109 & 117 & 200 & 30\\\end{pmatrix}\ and\ h(x, y) = \begin{pmatrix} -1 & 0 & 1\\-1 & 0 & 1\\-1 & 0 & 1\\\end{pmatrix} \end{equation*}\]

We have to move the kernel over each and every pixel of the image from top left to bottom. Placing a kernel over an image and taking an elementwise matrix multiplication of the kernel and chunk of image of the kernel shape. For most cases, we use odd shaped kernels. By using an oddly shaped kernel, we can place a center of the kernel to the center of the image chunk.

Now we try to start from the top right pixel, but since our kernel is 3 by 3, we don’t have any pixels that will be facing the 1st row of the kernel. So we have to work with the concept of padding or we will lose those pixels of the border. For the sake of simplicity, let’s take a zero padding.

\[\begin{equation} padded\ f(x, y) = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 10 & 11 & 20 & 30 & 0\\ 0 & 12 & 200 & 152 & 223 & 60 & 0 \\ 0 & 100 & 190 & 11 & 20 & 10 & 0\\ 0 & 102 & 207 & 102 & 223 & 50 & 0\\ 0 & 18 & 109 & 117 & 200 & 30 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{pmatrix} \end{equation}\]

Now the first chunk of image will be:

\[\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 10 \\ 0 & 12 & 200 \\ \end{pmatrix}\]

Now the convolution operation:

\[\begin{equation} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 10 \\ 0 & 12 & 200 \\ \end{pmatrix} * \begin{pmatrix} -1 & 0 & 1\\ -1 & 0 & 1\\ -1 & 0 & 1\\ \end{pmatrix}= 0*-1+0*0+0*1+0*- 1+1*0+10*1+0*-1+12*0+200*1 = 210 \end{equation}\]

Similarly, the final image will be like below after sliding through row then column:

\[\begin{pmatrix} 210 & 150 & 213 & 0 & 0\\ 400 & 61 & 43 & 0 & 0 \\ 597 & 51 & 0 & 0 & 0\\ 506 & 10 & 0 & 0 & 0 \\ 316 & 99 & 107 & 0 & 0\\ \end{pmatrix}\]

But we will set 255 to all values which exceeds 255.

A better visualization of a convolution operation can be seen by below gif(i don’t own this gif):-

Finally, visualizing our convoluted image:-

    ip = ImageProcessing()
    img = np.array([1, 10, 11, 200, 30, 12, 200, 152, 223, 60, 100,
                190, 11, 20, 10, 102, 207, 102, 223, 50, 18, 109, 117, 200, 30]).reshape(5, 5)
    cv = ip.convolve(img)
    ip.show(cv)

If we print the output of this code, i.e. cv, then we will see the array just like above.