<< Chapter < Page Chapter >> Page >

2. software implementation of the hough transform

2.1 approach

We first detect edges using the Sobel operator [1], and then we apply the Hough circle transform to detect circles in the image [2.]The following steps we took will be covered in more detail under section 2.2.

  1. Blurring image with the Gaussian kernel
  2. Using the Sobel operator to find edge points
  3. Applying Hough circle transform
  4. Processing the results of the transform

FIGHT ME.

Fig 2.1 From left to right: Original image, blurred image, image Edges, Hough transform results, processing the results of the Hough transform.

2.2 software implementation

Software implementation was done with Python. The following Python libraries were used.

  • Numpy version 1.10.1
  • Scipy version 0.16.0
  • OpenCV version 3.0.0

2.2.1 blurring the image with the gaussian kernel

Blurring the image removes noise and filters out background details. To do this, we blur the image with a Gaussian kernel.

Gaussian kernel.

Fig 2.2 5x5 Gaussian kernel with a standard deviation of 1

Code

def blur(img, blursize): """:param img: image to be blurred :param blursize: size of gaussian kernel to blur with:return: blurred image """# ============================= # Generate Gaussian kernel# ============================= gauss = cv2.getGaussianKernel(blursize, blursize/3)gauss = np.outer(gauss, gauss) # =============================# Filter with Gaussian kernel # =============================img = cv2.filter2D(img, -1, gauss) return img

2.2.2 using the sobel operator to find edge points

Edges occur at large changes in pixel value, so by finding local maximums in the image gradient’s magnitude, we can detect edge points. This concept is illustrated in 1 dimension (1D) in Fig 2.3.

edge.

Fig 2.3 Edges occur at large changes in pixel value, or, local maximums in the derivative.

Convolving an image with the Sobel operator gives us the approximate partial derivatives in the x and y directions. Let us define The Sobel operator as Sx for the x direction and Sy for the y direction, let our define our image as A, and let us define Bx and By as the partial x and partial y, respectively, derivative approximations of A.

sobel operators

Fig 2.4 Sobel operators for approximating partial x and partial y derivatives

gradient.

We can find the magnitude of gradient with equation 2.2, where the square and square root are element-wise operations.

magnitude

Now let E be a boolean matrix of the same dimensions as the image where if a pixel is an edge, then the boolean value for the pixel is True. We calculate this matrix by determining a threshold tmag and declaring every pixel whose gradient magnitude is at least tmag an edge pixel

Thresholded edges.

In our actual approach, we split the image into red, blue, and green channels. We perform edge detection on all 3 and recombine them with equation 2.4. This method allows us to find cleaner edges.

channels.

We can find the gradient of B with equation 2.5. Though it doesn’t factor into the method of edge detection used here, finding the gradient at edges is important for reducing computational complexity for the Hough transform.

Questions & Answers

how to create a software using Android phone
Wiseman Reply
how
basra
what is the difference between C and C++.
Yan Reply
what is software
Sami Reply
software is a instructions like programs
Shambhu
what is the difference between C and C++.
Yan
yes, how?
Hayder
what is software engineering
Ahmad
software engineering is a the branch of computer science deals with the design,development, testing and maintenance of software applications.
Hayder
who is best bw software engineering and cyber security
Ahmad
Both software engineering and cybersecurity offer exciting career prospects, but your choice ultimately depends on your interests and skills. If you enjoy problem-solving, programming, and designing software syste
Hayder
what's software processes
Ntege Reply
I haven't started reading yet. by device (hardware) or for improving design Lol? Here. Requirement, Design, Implementation, Verification, Maintenance.
Vernon
I can give you a more valid answer by 5:00 By the way gm.
Vernon
it is all about designing,developing, testing, implementing and maintaining of software systems.
Ehenew
hello assalamualaikum
Sami
My name M Sami I m 2nd year student
Sami
what is the specific IDE for flutter programs?
Mwami Reply
jegudgdtgd my Name my Name is M and I have been talking about iey my papa john's university of washington post I tagged I will be in
Mwaqas Reply
yes
usman
how disign photo
atul Reply
hlo
Navya
hi
Michael
yes
Subhan
Show the necessary steps with description in resource monitoring process (CPU,memory,disk and network)
samuel Reply
What is software engineering
Tafadzwa Reply
Software engineering is a branch of computer science directed to writing programs to develop Softwares that can drive or enable the functionality of some hardwares like phone , automobile and others
kelvin
if any requirement engineer is gathering requirements from client and after getting he/she Analyze them this process is called
Alqa Reply
The following text is encoded in base 64. Ik5ldmVyIHRydXN0IGEgY29tcHV0ZXIgeW91IGNhbid0IHRocm93IG91dCBhIHdpbmRvdyIgLSBTdGV2ZSBXb3puaWFr Decode it, and paste the decoded text here
Julian Reply
what to do you mean
Vincent
hello
ALI
how are you ?
ALI
What is the command to list the contents of a directory in Unix and Unix-like operating systems
George Reply
how can i make my own software free of cost
Faizan Reply
like how
usman
hi
Hayder
The name of the author of our software engineering book is Ian Sommerville.
Doha Reply
what is software
Sampson Reply
the set of intruction given to the computer to perform a task
Noor
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Hough transform object detection. OpenStax CNX. Dec 16, 2015 Download for free at http://legacy.cnx.org/content/col11937/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Hough transform object detection' conversation and receive update notifications?

Ask