pythonopencvimage-processingcomputer-visionlaplacianofgaussian

Is Laplacian of Gaussian for blob detection or for edge detection?


The following code is provided from (was asked to remove the link). But I was wondering how it exactly works. I was confused if this was considered edge detection or blob detection, as Wikipedia list the Laplacian of Gaussian (LoG) as blob detection.

Also, could somebody explain and provide a deeper explanation for why the absolute value is calculated and what is going on in the focus_stack() function?

#   Compute the gradient map of the image
def doLap(image):

    # YOU SHOULD TUNE THESE VALUES TO SUIT YOUR NEEDS
    kernel_size = 5         # Size of the laplacian window
    blur_size = 5           # How big of a kernal to use for the gaussian blur
                            # Generally, keeping these two values the same or very close works well
                            # Also, odd numbers, please...

    blurred = cv2.GaussianBlur(image, (blur_size,blur_size), 0)
    return cv2.Laplacian(blurred, cv2.CV_64F, ksize=kernel_size)

#
#   This routine finds the points of best focus in all images and produces a merged result...
#
def focus_stack(unimages):
    images = align_images(unimages)

    print "Computing the laplacian of the blurred images"
    laps = []
    for i in range(len(images)):
        print "Lap {}".format(i)
        laps.append(doLap(cv2.cvtColor(images[i],cv2.COLOR_BGR2GRAY)))

    laps = np.asarray(laps)
    print "Shape of array of laplacians = {}".format(laps.shape)

    output = np.zeros(shape=images[0].shape, dtype=images[0].dtype)

    abs_laps = np.absolute(laps)
    maxima = abs_laps.max(axis=0)
    bool_mask = abs_laps == maxima
    mask = bool_mask.astype(np.uint8)
    for i in range(0,len(images)):
        output = cv2.bitwise_not(images[i],output, mask=mask[i])

    return 255-output

Solution

  • EDIT: Cris Luengo is right. Ignore the part about edge detector.


    Laplacian of Gaussian(LoG) can be used as both edge detector and blob detector. I will skip the detailed mathematics and rationale, I think you can read them on a book or some websites here, here and here.

    To see why it can be used as both, let's look at its plot and kernel.

    enter image description here enter image description here

    If you have a blob with radius of 3 and value 1 centered at the kernel, and the background has value 0, you will have a very strong (negative) response. It is clear why it can do blob detection if the radius is set properly.

    How about edge detection? Well it is not like Sobel operator which gives you gradient and strong response for edges. Sobel operator does not give you accurate edges as the gradient usually rise and fall across a few pixels. Your edge would then be several pixels wide. To make it localize more accurate, we can find the pixel with maximum (or minimum) gradient locally. This implies its second derivative (Laplacian) should equal zero, or has a zero-crossing at that point.

    BeforeAfter

    You can see the processed image has both a light and dark band. The zero-crossing is the edge. To see this with a kernel, try sliding a perfect step edge across the kernel manually to see how the respond changes.

    For you second question, I guess the absolute is trying to find both light and dark blob (light blob, dark background; dark blob, light background) as they gives strong negative and strong positive response respectively. It then find the max across all images at each pixel location. For each output pixel, it uses the pixel at the image with the maximum response as output. I think his rationale is that pixels with strong impulse (small blob) are in-focus.

    He is using bitwise_not as a copy mechanism. It sets some pixels, specified by the mask, to the bitwise not of the source image. At the end, you would have output consisting of pixels from different sources, except that all of them have undergone bitwise not. To recover the true image, simply 'NOT' them again, as NOT(NOT(x)) = x. 255-x does exactly that. I think a copyTo would work too, not sure why he chose otherwise.

    Images taken from http://fourier.eng.hmc.edu/e161/lectures/gradient/node8.html.