The generalized Radon transform: Sampling, accuracy and memory considerations

Abstract

The generalized Radon (or Hough) transform is a well-known tool for detecting parameterized shapes in an image. The Radon transform is a mapping between the image space and a parameter space. The coordinates of a point in the latter correspond to the parameters of a shape in the image. The amplitude at that point corresponds to the amount of evidence for that shape. In this paper we discuss three important aspects of the Radon transform. The first aspect is discretization. Using concepts from sampling theory we derive a set of sampling criteria for the generalized Radon transform. The second aspect is accuracy. For the specific case of the Radon transform for spheres, we examine how well the location of the maxima matches the true parameters. We derive a correction term to reduce the bias in the estimated radii. The third aspect concerns a projection-based algorithm to reduce memory requirements.

Quantification of Microcapsules Deposited in Cotton Fabrics before and after Abrasion Using Fluorescence Microscopy

“…Objects with a circularity >1.15 can be due to broken capsules and/or released oils, due to clusters of microcapsules, or to a combination of both. Circles detection in noncircular objects was performed with the Radon algorithm, followed by automatic discrimination of inappropriate circles (e.g. those with a center outside the thresholded object).…”

Generalized Hough transform for 3D object recognition and visualization in integral imaging

“…[LHT]) in edge binary images [4,5] and it was later on extended to other analytical shapes (Circular Hough Transform [6] [CHT], Elliptical [7] Hough Transform [EHT]). Besides, in order to detect patterns with no analytical representation, the transformation was extended to what is known as Generalized Hough Transform (GHT) [8,9] which has proven to be useful in many applications either under its computational implementation [10][11][12][13][14] or its optical counterpart [15][16][17][18], with the possibility in the latter of achieving real-time [19], fully-invariant [20] pattern recognition.…”

Simultaneous automatic segmentation of multiple needles using 3D ultrasound for high-dose-rate prostate brachytherapy

“…A number of investigators have proposed line detection algorithms for the segmentation of single needles in 3D ultrasound images in vivo showing promising performance for specific needle‐guidance tasks . Techniques have been proposed based on orthogonal projections; geometric transformations such as parallel integral projections (PIP), the 3D Hough transform (3DHT), and the generalized Radon transform; and iterative methods such as random sample consensus (RANSAC) . These techniques have all been validated using image regions containing single needles; however, the algorithm requirements for HDR‐BT needle segmentation, as discussed by Buzurovic et al , have not been fully investigated.…”