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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

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
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The nanotechnology is as new science, to scale nanometric
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
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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.
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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.
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Smarajit Reply
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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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