What is Radon transform explain how it is used to obtain the projections of object?

Applying the Radon transform on an image f(x,y) for a given set of angles can be thought of as com- puting the projection of the image along the given angles. The resulting projection is the sum of the intensities of the pixels in each direction, i.e. a line integral. The result is a new image R(ρ,θ).

Is Radon transform linear?

e Radon transform is in fact a linear transformation, which can be seen by the fol- lowing calculations.

What is a Sinogram Radon transform?

The Radon transform data is often called a sinogram because the Radon transform of an off-center point source is a sinusoid. Consequently, the Radon transform of a number of small objects appears graphically as a number of blurred sine waves with different amplitudes and phases.

Why is Abel transform useful?

The Abel transform plays an important role in the theory of the spherical Fourier transform on synm1e’tric spaces of ‘the noncompac’t ‘type. Its role is analogous t:o. the role of ‘the Radon ‘transform in the theory of the ordinary Fourier transform on IRn. Therefore we first present the example of the ordin.

What is Radon function in Matlab?

The radon function computes projections of an image matrix along specified directions. A projection of a two-dimensional function f(x,y) is a set of line integrals. The radon function computes the line integrals from multiple sources along parallel paths, or beams, in a certain direction.

What is back projection CT?

Backprojection. The standard method of reconstructing CT slices is backprojection. This involves “smearing back” the projection across the image at the angle it was acquired. By smearing back all of the projections, you reconstruct an image.

What is Radon transform in CT?

The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans. A technique for using Radon transforms to reconstruct a map of a planet’s polar regions using a spacecraft in a polar orbit has also been devised (Roulston and Muhleman 1997).

How do you do a Radon transform in Matlab?

R = radon( I ) returns the Radon transform R of 2-D grayscale image I for angles in the range [0, 179] degrees. The Radon transform is the projection of the image intensity along a radial line oriented at a specific angle. R = radon( I , theta ) returns the Radon transform for the angles specified by theta .

How Hough Transform Detect lines Matlab?

Detect Lines in Images Using Hough Find the edges in the image using the edge function. Compute the Hough transform of the binary image returned by edge . [H,theta,rho] = hough(BW); Display the transform, H , returned by the hough function.

What are kernels in CT scan?

The kernel, also known as a convolution algorithm, refers to the process used to modify the frequency contents of projection data prior to back projection during image reconstruction in a CT scanner 1. This process corrects the image by reducing blurring 1.

How are CT images reconstructed?

CT makes use of filtered back projection reconstruction techniques, whereby each projection is convolved with a “filter”, and then back projected. When this procedure is performed for all 1000 or so projections, it is possible to achieve a perfect reconstruction of the scanned object.