Invariant characterisation of the Hough transform for pose estimation of arbitrary shapes

Abstract

In this paper, we develop a new formulation and methodology for including invariance in a general form of the Hough transform. Essentially, the transformations that control a shape's appearance are extracted using invariance, for arbitrary shapes with a continuous description. We ÿrst develop a formal deÿnition of the Hough transform mapping for arbitrary shapes and general transformations. We then include an invariant characterisation of shapes and develop and apply our new technique to extract shapes under similarity and a ne transformations. Our formulation and implementation is based directly on parametric curves and so avoids the use of indexed look-up tables. This confers the attributes of a continuous shape description avoiding discretisation problems inherent in earlier formulations. To obtain an invariant characterisation, each point in the model is related to a collection of other points deÿning a geometric arrangement. This characterisation does not require the computation of properties for lines or other primitives that compose the model, but is based solely on the local geometry of the points on shapes. The transformation is obtained by solving for the parameters of the curve according to an arrangement of points deÿned for a point in the image and a corresponding arrangement of points for a point in the model with the same invariant properties. The location parameters can be gathered in a 2D accumulator space independent of the transformation and of a shape's complexity. Experimental results show that the new technique is capable of extracting arbitrary shapes under occlusion and when the image contains signiÿcant noise. ?

Automatic detection of supporting device positioning in intensive care unit radiography

“…ET, NT, 3-10 pixels; FT, 15-25 pixels; Figure 8; cases 1 and 2). For this situation, the length of the tube in this tile is arbitrary, so a generalized HT is applied to solve this problem in order to accurately capture the tip (19,20). For the generalized HT, an arbitrary length of tube can be detected (Figure 8; case 3).…”

Segmentation in Echocardiographic Sequences using Shape-based Snake Model Combined with Generalized Hough Transformation

“…However, this equation is not suitable for direct implementation due to the computational complexity required to store and process the accumulator space defined by the translation parameters t and the transformation parameters A. To reduce the dimensionality of the accumulator space, Aguado et al [24] defines a function Q that establish the relationship:…”

Adaptive Hough transform for the detection of natural shapes under weak affine transformations

“…Aguado, 2002;Kimura and Watanabe, 2002;Ser and Siu, 1995;Fung et al, 1996), which from n image points produce only one incrementation in the array. They are usually fully invariant respective to the underlying geometric transformation and the parameters can be computed at once from image points, reducing therefore the number of superfluous operations and the computation time.…”

“…During the detection process, the elements of the accumulator array that are incremented are given by Aguado (2002) fðt; AÞjt ¼ x À Ax i ; juðxÞ À arg½Aðcosðx i Þ; sinðx i ÞÞ 0 j < du;…”