Optimal edge-based shape detection

Abstract

Abstract-We propose an approach to accurately detecting twodimensional (2-D) shapes. The cross section of the shape boundary is modeled as a step function. We first derive a one-dimensional (1-D) optimal step edge operator, which minimizes both the noise power and the mean squared error between the input and the filter output. This operator is found to be the derivative of the double exponential (DODE) function, originally derived by Ben-Arie and Rao [5]. We define an operator for shape detection by extending the DODE filter along the shape's boundary contour. The responses are accumulated at the centroid of the operator to estimate the likelihood of the presence of the given shape. This method of detecting a shape is in fact a natural extension of the task of edge detection at the pixel level to the problem of global contour detection. This simple filtering scheme also provides a tool for a systematic analysis of edge-based shape detection. We investigate how the error is propagated by the shape geometry. We have found that, under general assumptions, the operator is locally linear at the peak of the response. We compute the expected shape of the response and derive some of its statistical properties. This enables us to predict both its localization and detection performance and adjust its parameters according to imaging conditions and given performance specifications. Applications to the problem of vehicle detection in aerial images, human facial feature detection, and contour tracking in video are presented.

Car Detection in Aerial Images of Dense Urban Areas

“…For instance, the work proposed by Moon et al [20], [21], wherein they utilised the derivative of the doubleexponential filter to extract gradients and the work of Zheng et al [22], who used morphological structuring elements and a classifier to distinguish actual car pixels. In a similar manner, Eikvil et al [23] proposed a detection approach that separates regions with high probability to contain cars, followed by two stages of object classification exploiting multi-spectral images, geometric properties and road networks.…”

“…In urban scenes, cars are more likely to be found in road and parking areas [20]- [24]. The extraction of these areas prior to the detection process would eliminate a large number of false positives, which are produced as a result of the visual similarity among cars and other objects.…”

Novel Method for 3D Objects Retrieval

“…The same sample is also passed to the system for which the edge based features [14] are used. The obtained observations for the system is as illustrated below.…”

Automatic detection of archaeological sites using a hybrid process of Remote Sensing, Gis techniques and a shape detection algorithm

“…In [2], the step expansion filter (SEF) is derived as an optimal step edge filter. The SEF is the derivative of the double exponential (DODE) filter derived by [1]. The criterion used by [1] is to minimize the sum of the noise power and the mean squared error between input and output.…”

“…Additionally, edges with weak responses also contribute to the shape detection making the edge operator suitable for use in images which have low contrast in boundary regions. As stated in [1], the optimal edge operator is the piecewise derivative h´of the smoothing operator by the following relation in Eq. 1.…”