Project 2

• Prewitt Operator

Attached below is the function to perform the Prewitt operation on an image.

def prewitt_operator(image: ndarray, gaussian_filter_size: int, gaussian_standard_deviation: float) -> ndarray:
    """
    :param image: An np.ndarray() corresponding to the Pixel Intensity of the Image.
    :param gaussian_filter_size: An integer corresponding to kernel size of the gaussian filter to apply on image.
    :param gaussian_standard_deviation: A float corresponding to the standard deviation used to compute the gaussian filter to apply to image.
    :returns : An np.ndarray() of the image onto which the Prewitt filter has been applied.
    """
    image = cv2.GaussianBlur(image, (gaussian_filter_size,gaussian_filter_size), gaussian_standard_deviation)
    vertical_filter = np.array([[-1,0,1],[-1,0,1],[-1,0,1]])
    vertical_filtered_img = cv2.filter2D(image, -1, vertical_filter)
    
    hortizontal_filter = np.array([[-1,-1,-1],[0,0,0],[1,1,1]])
    hortizontal_filtered_img = cv2.filter2D(image, -1 , hortizontal_filter)
    
    abs_grad_x = cv2.convertScaleAbs(vertical_filtered_img)
    abs_grad_y = cv2.convertScaleAbs(hortizontal_filtered_img)
    
    gradient = cv2.addWeighted(abs_grad_x, 0.5, abs_grad_y, 0.5, 0)
    return gradient

Arguments:

1. image - An ndarray() corresponding to the pixel intensity of the image, read using functions such as cv2.imread()
2. gaussian_filter_size - An integer corresponding to the size of the kernel, it is used to compute the gaussian filter to apply to the image.
3. gaussian_standard_deviation - A float corresponding to the standard deviation used to compute the gaussian filter to be applied to the image.

Steps:

1. A grayscale image of the image is passed to
2. A gaussian filter is computed using arguments passed to the function.
3. A vertical and horizontal filter is identified to be applied to the image.
   1. The filters need to be selected in such a way that equal weightage is applied to the neighbouring elements of the pixel of interest.
4. The vertical and horizontal filters are applied to the image separately.
5. The magnitude of the two images (vectors) gives the result of the filter.

Result:

• Laplacian Operator

Attached below is the function to perform the Laplacian operation on an image.

def laplacian_operator(image: ndarray, gaussian_filter_size: int, gaussian_standard_deviation: float, kernel_size: int = 1) -> ndarray:
    """
    :param image: An np.ndarray() corresponding to the Pixel Intensity of the Image.
    :param gaussian_filter_size: An integer corresponding to the size of filter to construct the gaussian filter.
    :param gaussian_standard_deviation: A float corresponding to the standard deviation of the gaussian filter 
    which is to be applied on the image.
    :param kernel_size: An integer corresponding to the kernel size of the Laplacian filter to be applied on the image.
    :returns : An np.ndarray() of the image onto which the Laplacian filter has been applied.
    """
    image = cv2.GaussianBlur(image, (gaussian_filter_size, gaussian_filter_size), gaussian_standard_deviation)
    filtered_img = cv2.Laplacian(image, cv2.CV_16S, kernel_size)
    filtered_img = cv2.convertScaleAbs(filtered_img)
    return filtered_img

Arguments:

1. image: An np.ndarray() corresponding to the Pixel Intensity of the Image.
2. gaussian_filter_size: An integer corresponding to the size of the filter to construct the gaussian filter.
3. gaussian_standard_deviation: A float corresponding to the standard deviation of the gaussian filter
   which is to be applied to the image.
4. kernel_size: An integer corresponding to the kernel size of the Laplacian filter to be applied to the image.

Steps:

1. A grayscale image of the image is passed to
2. A gaussian filter is computed using arguments passed to the function.
3. A Laplacian filter is applied to the image using cv2.Laplacian()

Result:

• Laplacian vs Prewitt
  
• The Laplacian is a second-order derivative of the pixel intensity of an image, whereas the Prewitt operator is the first-order derivative.
• The Prewitt operator needs to be applied separately to both axes of an image, ie the output is dimensionally variant, whereas Laplacian is dimensionally invariant.
• The Accuracy of the Prewitt filter appears to be lower than the Laplacian filter.
• The Laplacian filter is better than Prewitt for this particular image.