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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


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


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.


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


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


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.


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

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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Akash Reply
it is a goid question and i want to know the answer as well
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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I'm interested in nanotube
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Ramkumar Reply
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Sravani Reply
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preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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