Generalized Hough Transform Research Articles

Efficient Pose Clustering Using a Randomized Algorithm

Pose clustering is a method to perform object recognition by determining hypothetical object poses and finding clusters of the poses in the space of legal object positions. An object that appears in an image will yield a large cluster of such poses close to the correct position of the object. If there are m model features and n image features, then there are O(m^3n^3) hypothetical poses that can be determined from minimal information for the case of recognition of three-dimensional objects from feature points in two-dimensional images. Rather than clustering all of these poses, we show that pose clustering can have equivalent performance for this case when examining only O(mn) poses, due to correlation between the poses, if we are given two correct matches between model features and image features. Since we do not usually know two correct matches in advance, this property is used with randomization to decompose the pose clustering problem into O(n^2) problems, each of which clusters O(mn) poses, for a total complexity of O(mn^3) . Further speedup can be achieved through the use of grouping techniques. This method also requires little memory and makes the use of accurate clustering algorithms less costly. We use recursive histograming techniques to perform clustering in time and space that is guaranteed to be linear in the number of poses. Finally, we present results demonstrating the recognition of objects in the presence of noise, clutter, and occlusion.

Detectability, uniqueness, and reliability of eigen windows for stable verification of partially occluded objects

This paper describes a method for recognizing partially occluded objects for bin-picking tasks using eigenspace analysis, referred to as the eigen window method, that stores multiple partial appearances of an object in an eigenspace. Such partial appearances require a large amount of memory space. Three measurements, detectability, uniqueness, and reliability, on windows are developed to eliminate redundant windows and thereby reduce memory requirements. Using a pose clustering technique, the method determines the pose of an object and the object type itself. We have implemented the method and verified its validity.

A chip-set for the Generalized Hough Transform

This paper describes the architecture of a chip-set that can be adopted in systems for object recognition based on the Generalized Hough Transform (GHT). The targeted applications aim at the real-time localization of two-dimensions objects of arbitrary shape not analytically described: this system has a throughput allowing for real-time operation on standard television signals. The characteristics of the GHT recognition process, aimed at generic bi-dimensional shapes, have been carefully exploited in order to map into silicon this transformation, so far considered too complex for a VLSI implementation. A functional description of the chip-set modules is given; the architectural aspects are analysed, together with the results of the prototyping phase, which addresses the problems of VLSI integration.

Colour image detection and matching using modified generalised Hough transform

A new approach to 2-dimensional (2D) colour-image detection and matching using a modified version of the generalised Hough transform (GHT) is proposed. In the conventional GHT, the useful colour information existing in the input image and the relationship between each pixel and its neighbourhood are not used. Furthermore, lighting changes in the image are not usually considered. Therefore, the conventional GHT is seldom applied to colour images. In the proposed approach, lighting changes are removed using normalised colour values. Next, certain critical pixels of an input colour image whose neighbourhoods have larger variances of normalised colour values are extracted. For each critical pixel, a feature vector, which includes the normalised colour values of the pixel as well as those of the pixel's neighbours, is then constructed. A modified voting rule for the GHT is therefore proposed which is based on a similarity-measure function of the feature vectors. High maximum peaks in the cell array are searched finally as the result. The proposed method is robust for colour-image detection and matching in noisy, occlusive, and lighting-change environments, as demonstrated by experimental results.

Chord-tangent transformation for object recognition

The problem of recognizing planar images in two-dimensional (2D) space has remained a problem of significant interest in computer vision for the last three decades. The Generalized Hough Transform has emerged as one of the more promising techniques because of its robustness to incomplete data and additive noise. However, the Generalized Hough transform is not well suited for similarity transformation because the parameters of scale and rotation cannot be solved using unary tangent information. In this paper, a new technique is introduced which uses a simple transformation of pairwise tangent information to allow for the direct computation of the parameters of scale and rotation and thus a more precise estimate of the translation parameters. This method shares many of the same advantages of the Generalized Hough Transform, while performing with greater efficiency and accuracy. This technique is applied to a database of objects, where the test object is a composite of model instances, having undergone similarity transformation, and in the presence of both noise and occlusion. The results are compared with that of the Generalized Hough Transform, and a critical analysis of the two methods is presented.

A New Generalized Hough Transform for the Detection of Irregular Objects

In this paper, we introduce a new generalized Hough transform for the recognition of nonanalytic objects in a 2-D image. The main idea of our approach is to use pairs of boundary points with the same gradient angle to derive some rotation-invariant parameters to effect the fast Hough transform. Each voting to the Hough domain is contributed by a pair of edge pixels with the same gradient angle. The primary obstacle to using the Hough techniques, a large memory requirement, is overcome by our new voting approach. The conventional 4-D Hough domain is significantly reduced to a 2-D domain. This approach provides an easy method for determining the parameters of the object in question and an extremely effective solution for eliminating false votes in the transform.

Pattern recognition by graph matching using the Potts MFT neural networks

This paper is concerned with programming of the Potts mean field theory neural networks for pattern recognition by homomorphic mapping of the attributed relational graphs (ARG). In order to generate the homomorphic mapping from the scene relational graph to the model graph, we make use of the recently introduced [Suganthan, Technical Report, Nanyang Technical University (1994)] compatibility functions in relation to the Hopfield network. An efficient pose clustering algorithm is used to separate and localize different occurrences of any particular object model in the scene. The pose clustering algorithm also eliminates spurious hypotheses generated by the network and resolves ambiguities in the final interpretation. The performance of the proposed approach to pattern recognition by homomorphism is demonstrated using a number of line patterns, silhouette images and circle patterns.

SYSTOLIC MERGING AND RANKING OF VOTES FOR THE GENERALIZED HOUGH TRANSFORM

In this paper we present and analyze a systolic structure to support the Generalized Hough Transform. Among the structural methods for object recognition, this transform is well established for its flexibility and noise immunity. Its use in actual systems has been however limited by the computational cost associated with the management of votes. Previous work has shown that a limited amount of memory can substitute the large address space required for building the histogram of votes. The systolic queue here introduced substitutes the address space required in a M- dimensional voting process, where the quantization of each dimension into Q bins yields a space complexity O(QM). An N-stage queue uses 3 M log(Q) memory bits at each stage and is capable of accumulating the incoming votes on the fly. The flow of data within the queue is designed to minimize the probability that new votes are lost because of overflow. We derive analytic expressions for the growth of the queue during the set-up period and for the time each new vote spends within the queue if it is not accumulated; furthermore, we show the conditions for the arrival times of a couple of coincident addresses to be detected and merged. The analysis of the time behaviour of the queue supports the experimental evidence that such a structure performs the accumulating process very reliably. A VLSI integrated circuit embedding a 50-stage queue is the third in a chip-set for the real time implementation of the Generalized Hough Transform.

Self-organizing Hopfield network for attributed relational graph matching

Although the analogue Hopfield model has been shown to be a plausible approach for solving combinatorial optimization problems such as the travelling salesman problem (TSP), it has not been effective in solving the object recognition problem by attributed relational graph matching, for many reasons. However, we 1 recently enhanced the performance of the Hopfield network in attributed relational graph (ARG) matching by employing suitable energy and compatibility functions, a biased network initialization scheme and a hypothesis interpretation scheme using an efficient pose clustering algorithm. However, to generate the desired mapping, there is a need to fine tune many parameters that are highly dependent upon the model and scene under consideration. In this paper, a self-organizing Hopfield network is introduced that learns most of the network parameters and eliminates the need for specifying them a priori. To adaptively estimate the energy function parameter, a Liapunov indirect method based learning approach is employed. Other variables, such as the temperature parameter and the convergence criterion, are heuristically determined. The proposed self-organizing network is applied to solve problems such as line patterns, silhouette images and circle pattern recognition. Its superior performance over the fixed weight model is also demonstrated.

Pattern recognition by homomorphic graph matching using Hopfield neural networks

The application of the Hopfield neural network as a constraint satisfaction network for pattern recognition is investigated in this paper. Suitable energy and compatibility functions are introduced for pattern recognition by homomorphic attributed relational graph (ARG) matching. Although many computer vision problems have been traditionally formulated as combinatorial optimization problems, most of them can be reduced to that of finding the nearest local minimum of an objective function. In this paper, a novel network initialization strategy is applied to achieve the desired complexity reduction. Further, a method to verify and localize the hypotheses generated by the Hopfield network is also presented using an efficient pose clustering algorithm. The performance of the connectionist approach to pattern recognition by homomorphic relational graph matching is demonstrated using a number of line patterns, silhouette images and circle patterns.

An automated computer vision and robotics-based technique for 3-D flexible biomolecular docking and matching.

The generation of binding modes between two molecules, also known as molecular docking, is a key problem in rational drug design and biomolecular recognition. Docking a ligand, e.g., a drug molecule or a protein molecule, to a protein receptor, involves recognition of molecular surfaces as molecules interact at their surface. Recent studies report that the activity of many molecules induces conformational transitions by 'hinge-bending', which involves movements of relatively rigid parts with respect to each other. In ligand-receptor binding, relative rotational movements of molecular substructures about their common hinges have been observed. For automatically predicting flexible molecular interactions, we adapt a new technique developed in Computer Vision and Robotics for the efficient recognition of partially occluded articulated objects. These type of objects consist of rigid parts which are connected by rotary joints (hinges). Our approach is based on an extension and generalization of the Geometric Hashing and Generalized Hough Transform paradigm for rigid object recognition. Unlike other techniques which match each part individually, our approach exploits forcefully and efficiently enough the fact that the different rigid parts do belong to the same flexible molecule. We show experimental results obtained by an implementation of the algorithm for rigid and flexible docking. While the 'correct', crystal-bound complex is obtained with a small RMSD, additional, predictive 'high scoring' binding modes are generated as well. The diverse applications and implications of this general, powerful tool are discussed.

Motion estimation methods and noisy phenomena

In an infrared surveillance system (which must detect remote sources and thus has a very low resolution) in an aerospace environment, the estimation of the cloudy sky velocity should lower the false alarm rate in discriminating the motion between various moving shapes by means of a background velocity map. The optical flow constraint equation, based on a Taylor expansion of the intensity function, is often used to estimate the motion for each pixel. One of the main problems in motion estimation is that, for one pixel, the real velocity cannot be found because of the aperture problem. Another kinematic estimation method is based on a matched filter [generalized Hough transform (GHT)]: it gives a global velocity estimation for a set of pixels. On the one hand we obtain a local velocity estimation for each pixel with little credibility because the optical flow is so sensitivity to noise; on the other hand, we obtain a robust global kinematic estimation, the same for all selected pixels. This paper aims to adapt and improve the GHT in our typical application in which one must discern the global movement of objects (clouds), whatever their form may be (clouds with hazy edges or distorted shapes or even clouds that have very little structure). We propose an improvement of the GHT algorithm by segmentation images with polar constraints on spatial gradients. One pixel, at timet, is matched with another one at timet + ΔT, only if the direction and modulus of the gradient are similar. This technique, which is very efficient, sharpens the peak and improves the motion resolution. Each of these estimations is calculated within windows belonging to the image, these windows being selected by means of an entropy criterion. The kinematic vector is computed accurately by means of the optical flow constraint equation applied on the displaced window. We showed that, for small displacements, the optical flow constraint equation sharpens the results of the GHT. Thus a semi-dense velocity field is obtained for cloud edges. A velocity map computed on real sequences with these methods is shown. In this way, a kinematic parameter discriminates between a target and the cloudy background.

A fuzzy probabilistic model for the generalized Hough transform

A fuzzy-probabilistic model of the generalized Hough transform (GHT) based on qualitative labeling of scene features is presented. Qualitative labeling of scene features is shown to be effective in pruning the search space of possible scene interpretations and also reducing the number of spurious interpretations explored by the GHT. Qualitative labeling of scene features is shown to result in the formulation of a weighted generalized Hough transform (WGHT) where each match of a scene feature with a model feature is assigned a weight based on the qualitative attributes assigned to the scene feature. These weights are looked upon as membership function values for the fuzzy sets defined by these qualitative attributes. A fuzzy-probabilistic model for the WGHT is presented. Analytical expressions for the probability of accumulation of random votes are derived for the WGHT and compared with the corresponding expressions for the conventional GHT. The WGHT is shown to perform better than the conventional GHT. Experimental results on intensity and range images are presented. >

Curve fitting approach for tangent angle and curvature measurements

The measures of tangent angle and curvature of a digital curve play an important role in image analysis such as corner detection, 1D shape representation and shape signature in the Generalized Hough Transform. Instead of using the discrete measurement approach, the least-squares method is employed to fit known digital points to two cubic polynomial functions, one with y = f( x) that minimizes the sum of the vertical distances and the other with x = g( y) that minimizes the sum of the horizontal distances from the known points to the approximated curve. The tangent angle and curvature are therefore directly computable from the first- and second-order derivatives of the continuous functions. Hybrid procedures are also proposed to select the better curve from f and g for accurate evaluation of tangent angle and curvature. Experimented results on both analytic curves and real-world images are included.

Edge replacement in the recognition of occluded objects

The Generalized Hough Transform recognizes objects more successfully when all edges are visible. To facilitate recognition, this paper introduces a preliminary Generalized Hough process that restores edges which were invisible because of occlusion or because of lack of contrast between occluding and occluded areas. Space and time complexity of Generalized Hough processes are reduced by chained hashing techniques. Experimental results show that recognition of occluded objects via a Generalized Hough Transform is improved if occluding objects are first recognized and subtracted out of the input picture, and occluded edges are then reconstructed prior to recognition of occluded objects.

The Generalized Hough Transform on Mesh-Connected Computers

This work analyzes the computational complexity of the Generalized Hough Transform (GHT) on a mesh-connected (MCC) and introduces practical algorithms for bidimensional shape recognition useful in real situations, and not just in asymptotic cases. This paper shows how to map such a transform onto a massive parallel computer that consists of a mesh of 4-connected processing elements (PEs). While a class of algorithms relying on general purpose data movements techniques has time complexity O( Rn log n) on an n × n MCC under the SIMD bit model, R being the number of points used to describe the shape, an important criterion implicitly embedded in the transform is not reflected in such implementations: namely, the locality of the transform with respect to the input image. Indeed, most shapes are bound by a circle having a radius d usually much smaller than the linear dimension of the mesh. This paper shows how an efficient implementation of the GHT can be obtained using this geometric constraint. Two classes of algorithms are introduced; both exhibit an asymptotic complexity O( Rd 2 log n) which is a function of the region enclosing the sought for shape. The derivation of exact time costs both for the standard implementations and for the new ones establishes the break-even point for any problem size. The proposed algorithms outperform the standard ones in all practical situations.

Directional mathematical morphology and reformalized Hough transformation for the analysis of topographic maps

One of the most difficult and important problems encountered in the automatic digitizing of graphical topographic maps is the identification and separate digitizing of different kinds of features. Essentially, in topographic maps, there are two kinds of geometric features: linear features, such as roads and railways that have an arbitrary length, and symbols, which indicate a type of building or area of land usage or even numerical information. These two types of features are extracted and recognized by using methods based on multiangled parallelism (MAP). The MAP operation method performs parallel calculation on directional feature planes. The linear features are extracted using erosion-dilation operations on the directional feature planes, and the symbols are extracted using a reformalized and parallel version of the generalized Hough transformation on the same directional planes, which is called the MAP matching method. The methods have been applied to a 1/25000 scale map. >

Linear generalized Hough transform and its parallelization

Abstract The Generalized Hough Transform (GHT) proposed by Ballard 1 is an effective method for recognizing objects of arbitrary shape. It converts a problem of global pattern matching into local peak searching. However, the GHT has difficulty in handling occluded objects. It also suffers from the congestion at the single peak point when attempting its potential parallelization. In this paper, we present a Linear Generalized Hough Transform (LIGHT) in which a linear numeric pattern is used to replace the single peak in the GHT. The LIGHT is more capable of detecting partially occluded objects. Moreover, it is well-suited for parallelization, especially on SIMD array processors. Several sequential and parallel LIGHT algorithms and our preliminary results are presented. The impact of noise on the effectiveness of the LIGHT algorithm is studied. The result for parallel implementation is obtained from an SIMD onedimensional array processor (the AIS-4000 Vision Processor with 512 processing elements). A speed-up factor of two orders of magnitude is achieved.

Qualitative features and the generalized hough transform

In this paper we show how the use of qualitative features can enhance the performance of recognition and localization techniques, in particular, the Generalized Hough Transform. Qualitative features (i.e. scene features with qualitative attributes assigned to them) are shown to be effective in pruning the search space of possible scene interpretations and also reducing the number of spurious interpretations explored by the recognition and localization technique. The redundancy of the computed transform and the probability of spurious peaks of significant magnitude due to random accumulation of evidence are two criteria by which the performance of the Generalized Hough Transform is judged. The straightforward Generalized Hough Transform shows a high probability of spurious peaks of significant magnitude even for small values of redundancy and small magnitude of the search space of scene interpretations. The use of qualitative features enables us to come up with a weighted Generalized Hough Transform where each match of a scene feature with a model feature is assigned a weight based on the qualitative attributes assigned to the scene feature. These weights could be looked upon as membership function values for the fuzzy sets defined by these qualitative attributes. Analytic expressions for the probability of accumulation of random events within a bucket are derived for the weighted Generalized Hough Transform and compared with the corresponding expression for the straightforward Generalized Hough Transform. The weighted Generalized Hough Transform is shown to perform better than the straightforward Generalized Hough Transform. An experiment for the recognition of polyhedral objects from range images is described using dihedral junctions as features for matching and pose computation. The experimental results bring out the advantages of the weighted Generalized Hough Transform over the straightforward Generalized Hough Transform.

Generalizing the generalized hough transform

We present a new method for model based recognition of articulated objects in cluttered scenes. The objects consist of rigid parts connected by rotary or prismatic joints. Our method is based on an extension of the Generalized Hough Transform paradigm. It is applicable to various viewing transformations. Unlike previous methods no significant degradation is expected in performance for recognition of articulated objects compared with the recognition of rigid objects containing a similar amount of information.