Using the generalized Radon transform for detection of curves in noisy images

In this paper the discrete generalized Radon transform will be investigated as a tool for detection of curves in noisy digital images. The discrete generalized Radon transform maps an image into a parameter domain, where curves following a specific parameterized curve form will correspond to a peak in the parameter domain. A major advantage of the generalized Radon transform is that the curves are allowed to intersect. This enables a thresholding algorithm in the parameter domain for simultaneous detection of curve parameters. A threshold level based on the noise level in the image is derived. A numerical example is presented to illustrate the theory. 1. INTRODUCTION In recent years the Hough transform [1] and the related Radon transform [2] have received much attention. These two transforms are able to transform two dimensional images with lines into a domain of possible line parameters, where each line in the image will give a peak positioned at the corresponding line parameters. T..

Detection of Lines with Wiggles using the Radon Transform

The discrete Radon transform is a useful tool in image processing for detection of lines (or in general curves) in digital images. One of the key properties of the discrete Radon transform is that a line in an image is transformed into a peak in the parameter domain, where the position of the peak corresponds to the line parameters. What often is needed, is to determine whether a Radon transform based curve detection algorithm will work in presence of noise. Lately analytical expressions for the probability of detecting a curve in presence of additive noise has been analyzed, and in this paper another kind of noise is analyzed theoretically, namely that the lines in the images might not be perfectly linear but include some random misalignment, here called wiggles. 1. INTRODUCTION The Radon transform can be defined in various ways. In general image processing the lines are often parameterized using normal parameters [1], and in seismic signal processing the ø -p transform or slant stac..

Estimation of the noise contributions from Blank, Transmission and Emission scans in PET

This work determines the relative importance of noise from blank (B), transmission (T) and emission (E) scans in PET using a GE Advance scanner on a 20 cm cylinder, a brain phantom, and a torso-like ellipse (18/35 cm) with examples of human scans (brain O-15 water and F-18 FDG, heart FDG). Phantom E scans were acquired in both 2D and 3D modes as decay series with C-11 or F-18 over 36 decades of Noise Equivalent Counts (NEC). B and T scans were made using two pin sources (ß500 MBq total) over 64-32768 sec. In humans only a limited subset was available. In homogeneous phantoms normalized variance (var) was estimated from pixel distributions in single images. In other objects, including the human studies, calulations were performed on differences of paired images. In all cases a fit was made to a simple noise model. The cylinder data show expected relations of T to B noise proving the adequacy of B scan times 20 min for most purposes. For the brain phantom, a contour plot is provided for..