Image Convolution and Edge Detection

Assignment number 2 in Computer Vision & Image Proccessing course. All tasks and functions were written in the ex2_utils.py file and they were all tested in the ex2_main.py file.

Using Python and the OpenCV library, implementation of:

Convolution
Image derivatives
Image Blurring
Edge detection via LoG zero-crossing
Hough Circles
Bilateral filter

Convolution

Comparing 2D Convolution Output to OpenCV

MSE: 0.00028858193628147563
Max Error: 0.4800071418285348

Image derivatives

Calculate gradient of an image. An image derivative - gradient - is defined as the change in the pixel value of an image.

Directions (angles) / Magnitude

Image Blurring

Image blurring is achieved by convolving the image with a low-pass filter kernel. It is useful for removing noise. It actually removes high frequency content (eg: noise, edges) from the image. So edges are blurred a little bit in this operation (there are also blurring techniques which don't blur the edges). Here we are blurring an image using a Gaussian kernel, my implementation.

OpenCV blurred	My blurred

	MSE:0.001328

Edge detection via LoG zero-crossing

In edge detection, we find the boundaries or edges of objects in an image, by determining where the brightness of the image changes dramatically. Edge detection can be used to extract the structure of objects in an image. If we are interested in the number, size, shape, or relative location of objects in an image, edge detection allows us to focus on the parts of the image most helpful, while ignoring parts of the image that will not help us. Detecting edges using "ZeroCrossingLOG" method - Zero-Crossing Detector Using the Laplacian of Gaussian (LoG) Filter

Comparing LoG zero-crossing Output to OpenCV

Hough Circles:

The circle Hough Transform (CHT) is a basic feature extraction technique used in digital image processing for detecting circles in imperfect images. The circle candidates are produced by “voting” in the Hough parameter space and then selecting local maxima in an accumulator matrix. Find Circles in an image using a Hough Transform algorithm extension.

Original	Output	Original	Output

	Time[Mine]: 43.060 sec [CV]: 0.051 sec		Time[Mine]: 0.664 sec [CV]: 0.004 sec

	Time[Mine]: 1.766 sec [CV]: 0.005 sec		[Mine]: 2.415 sec [CV]: 0.001 sec

	[Mine]: 3.333 sec [CV]: 0.006 sec