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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Hough transform object detection. OpenStax CNX. Dec 16, 2015 Download for free at http://legacy.cnx.org/content/col11937/1.1
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