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Radon transform is also known as projection transform, Raysum transform, and line integral transform. Radon transform [6] is one of the techniques used to detect features within the image. This technique is widely used in tomography to reconstruct an object from different projections for medical applications. The Radon transform is translation and rotation invariants, and thus it preserves the variations in pixel intensities. In practice, Radon transform has been used to project the 2D image into Radon space before subjected to other transforms.

The Radon transform is based on the parameterization of the straight line of an image domain and on the evaluation of the integrals of the image along these straight lines. The Radon transform helps the implementation of very effective detection algorithms; however, it does not provide itself sufficient information for recognition purposes. [1] Fortunately, due to inherent properties of the Radon transform, it is a useful tool to capture the directional features of the images. [2]

The Radon transform has been widely applied for deriving the local features in edge detection, textural classification, retrieve the image in computer tomography, face recognition [2 -3, 5] and also in medical images [4].

In Radon transform, Equation 4274a is used to represent a line,
         x cos θ + y sin θ = ρ ---------------------------------- [4274a]
where,          
         x (or, θ) -- the angle from the x-axis,
         y (or, ρ) -- the distance between the line and the point of origin.

Therefore, the projection is performed along each straight line with specific values of ρ and θ.

Figure 4274 shows some examples of patterns obtained from Radon transform. For instance, the center pattern has a narrow but strong response in the central area of ρ. Donut presents two bands around the center area with wider responses. Edge-ring exhibits a strong response along the border of the response band.

Edge-ring
	(a.A)	(a.B)	(a.C)
Center
	(b.A)	(b.B)	(b.C)
Donut
	(c.A)	(c.B)	(c.C)
Edge-loc
	(d.A)	(d.B)	(d.C)
Loc
	(e.A)	(e.B)	(e.C)
Random
	(f.A)	(f.B)	(f.C)
Scratch
	(g.A)	(g.B)	(g.C)

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Extract the projection results by following Radon transform. code:          
         
Input:         
         
Output (Note that the profile at 45 degree is very different from the ones at 0 and 90 degrees because of the contrast outside the disk is valued by "1" by the program. Those values also added artificial background into the profiles at 0 and 90 degrees):         
         

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Extract the projection results by following extracting images in three colors (blue, green, and red) and with Radon transform. code:          
         
Input:         
         
Output:         
         
Input and code:         
         
         
New output (the edge ring shows clearly):         
         

[1] E. Magli, G. Olma, and L. Lo Presti, “Pattern recognition by means of the Radon transform and the continuous wavelet transform, Signal Processing, Vol. 73, (1999), p. 277-289.
[2] J. A. Dargham, A. Chekima, E. Moung, and S.Omatu: Radon transform for face recognition. Artificial Life and Robotics, 15(3), (2010), p.359– 362.
[3] D. V. Jadhav, and R. S. Holambe, “ Feature extraction using Radon and wavelet transforms with application to face recognition. Neurocomputing, 72(7-9), (2009), p. 1951–1959.
[4] U, R. Acharya, C. K. Chua, E. Y. K. Ng, W. Yu, and C.Chee: Application of higher order spectra for the identification of diabetes retinopathy stages. Journal of Medical Systems, 32(6), (2008), p. 481–488.
[5] Hasimah Ali, Vinothan Sritharan, Muthusamy Hariharan, Siti Khadijah Zaaba, Mohamed Elshaikh, Feature extraction using Radon transform and Discrete Wavelet Transform for facial emotion recognition, 2016 2nd IEEE International Symposium on Robotics and Manufacturing Automation (ROMA), DOI: 10.1109/ROMA.2016.7847840, 2016.
[6] R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. Harlow, U.K.:Prentice-Hall, 2008.