Subspace-based Line Detection Research Articles

Subspace-Based and DIRECT Algorithms for Distorted Circular Contour Estimation

Circular features are commonly sought in digital image processing. The subspace-based line detection (SLIDE) method proposed to estimate the center and the radius of a single circle. In this paper, we introduce a novel method for estimating several radii while extending the circle estimation to retrieve circular-like distorted contours. Particularly, we develop and validate a new model for virtual signal generation by simulating a circular antenna. The circle center is estimated by the SLIDE method. A variable speed propagation scheme toward the circular antenna yields a linear phase signal. Therefore, a high-resolution method provides the radius. Either the gradient method or the more robust combination of dividing rectangles and spline interpolation can extend this method extend this method for free form object segmentation. The retrieval of multiple non concentric circles and rotated ellipses is also considered. To evaluate the performance of the proposed methods, we compare them with a least-squares method, Hough transform, and gradient vector flow. We apply the proposed method to hand-made images while considering some real-world images.

Array Processing and Fast Optimization Algorithms for Distorted Circular Contour Retrieval

A specific formalism for virtual signal generation permits to transpose an image processing problem to an array processing problem. The existing method for straight-line characterization relies on the estimation of orientations and offsets of expected lines. This estimation is performed thanks to a subspace-based algorithm called subspace-based line detection (SLIDE). In this paper, we propose to retrieve circular and nearly circular contours in images. We estimate the radius of circles and we extend the estimation of circles to the retrieval of circular-like distorted contours. For this purpose we develop a new model for virtual signal generation; we simulate a circular antenna, so that a high-resolution method can be employed for radius estimation. An optimization method permits to extend circle fitting to the segmentation of objects which have any shape. We evaluate the performances of the proposed methods, on hand-made and real-world images, and we compare them with generalized Hough transform (GHT) and gradient vector flow (GVF).

Contour Estimation by Array Processing Methods

This work is devoted to the estimation of rectilinear and distorted contours in images by high-resolution methods. In the case of rectilinear contours, it has been shown that it is possible to transpose this image processing problem to an array processing problem. The existing straight line characterization method called subspace-based line detection (SLIDE) leads to models with orientations and offsets of straight lines as the desired parameters. Firstly, a high-resolution method of array processing leads to the orientation of the lines. Secondly, their offset can be estimated by either the well-known method of extension of the Hough transform or another method, namely, the variable speed propagation scheme, that belongs to the array processing applications field. We associate it with the method called "modified forward-backward linear prediction" (MFBLP). The signal generation process devoted to straight lines retrieval is retained for the case of distorted contours estimation. This issue is handled for the first time thanks to an inverse problem formulation and a phase model determination. The proposed method is initialized by means of the SLIDE algorithm.

Estimation of time-varying velocities of moving objects by time-frequency representations

An approach to the estimation of motion parameters of moving objects in a video-sequence, by using the SLIDE (subspace-based line detection algorithm) algorithm, is considered. The proposed procedure projects video-frames to the coordinate axes, in order to obtain synthetic images containing information about the motion parameters. These synthetic images are mapped to the FM signals by using constant mu-propagation. The problem of velocity estimation is reduced to the instantaneous frequency (IF) estimation. IF estimators, based on time-frequency (TF) representations, are used. Three TF representations: spectrogram (SPEC), Wigner distribution (WD), and S-method (SM), are used and compared to this aim. A tradeoff between concentration of the TF representation (velocity estimation accuracy) and reduction of the cross-terms (possibility for estimation of the multiple objects parameters) is achieved by the SM. A performance analysis of the algorithm is done. Theoretical results are illustrated on several numerical examples.

Estimation of multiple 2-D uniform motions by SLIDE: subspace-based line detection

A technique is proposed for estimating the parameters of two-dimensional (2-D) uniform motion of multiple moving objects in a scene, based on long-sequence image processing and the application of a multiline fitting algorithm. Plots of the vertical and horizontal projections versus frame number give new images in which uniformly moving objects are represented by skewed band regions, with the angles of the skew from the vertical being a measure of the velocities of the moving objects. For example, vertical bands will correspond to objects with zero velocity. An algorithm called subspace-based line detection (SLIDE) can be used to efficiently determine the skew angles. SLIDE exploits the temporal coherence between the contributions of each of the moving patterns in the frame projections to enhance and distinguish a signal subspace that is defined by the desired motion parameters. A similar procedure can be used to determine the vertical velocities. Some further steps must then be taken to properly associate the horizontal and vertical velocities.

On the magic of SLIDE

Subspace-based line detection (SLIDE) is a novel approach for straight line fitting that has recently been suggested by Aghajan and Kailath. It is based on an analogy made between a straight line in an image and a planar propagating wavefront impinging on an array of sensors. Efficient sensor array processing algorithms are used to detect the parameters of the line. SLIDE is computationally cheaper than the Hough transform, but it has not been clear whether or not this is a magical free bonus. In particular, it has not been known how the breakpoints of SLIDE relate to those of the Hough transform. We compare the failure modes and limitations of the two algorithms and demonstrate that SLIDE is significantly less robust than the Hough transform.

Estimation of skew angle in text-image analysis bySLIDE: Subspace-based line detection

A new signal processing method is developed for estimating the skew angle in text document images. Detection of the skew angle is an important step in text processing tasks such as optical character recognition (OCR) and computerized filing. Based on a recently introduced multiline-fitting algorithm, the proposed method reformulates the skew detection problem into a special parameter-estimation framework such that a signal structure similar to the one in the field of sensor array processing is obtained. In this framework, straight lines in an image are modeled as wavefronts of propagating planar waves. Certain measurements are defined in this virtual propagation environment such that the large amount of coherency that exists between the locations of the pixels on parallel lines is exploited to enhance a subspace in the space spanned by the measurements. The well-studied techniques of sensor array processing (e.g., the ESPRIT algorithm) are then exploited to produce a closed form and high-resolution estimate for the skew angle.

SLIDE: subspace-based line detection

An analogy is made between each straight line in an image and a planar propagating wavefront impinging on an array of sensors so as to obtain a mathematical model exploited in recent high resolution methods for direction-of-arrival estimation in sensor array processing. The new so-called SLIDE (subspace-based line detection) algorithm then exploits the spatial coherence between the contributions of each line in different rows of the image to enhance and distinguish a signal subspace that is defined by the desired line parameters. SLIDE yields closed-form and high resolution estimates for line parameters, and its computational complexity and storage requirements are far less than those of the standard method of the Hough transform. If unknown a priori, the number of lines is also estimated in the proposed technique. The signal representation employed in this formulation is also generalized to handle grey-scale images as well. The technique has also been generalized to fitting planes in 3-D images. Some practical issues of the proposed technique are given. >