Changming Sun | CSIRO - Academia.edu (original) (raw)

Papers by Changming Sun

IEEE Transactions on Pattern Analysis and Machine Intelligence

Interest point detection is one of the most fundamental and critical problems in computer vision ... more Interest point detection is one of the most fundamental and critical problems in computer vision and image processing. In this paper, we carry out a comprehensive review on image feature information (IFI) extraction techniques for interest point detection. To systematically introduce how the existing interest point detection methods extract IFI from an input image, we propose a taxonomy of the IFI extraction techniques for interest point detection. According to this taxonomy, we discuss different types of IFI extraction techniques for interest point detection. Furthermore, we identify the main unresolved issues related to the existing IFI extraction techniques for interest point detection and any interest point detection methods that have not been discussed before. The existing popular datasets and evaluation standards are provided and the performances for eighteen state-of-the-art approaches are evaluated and discussed. Moreover, future research directions on IFI extraction techniques for interest point detection are elaborated.

IEEE Access, 2019

In this paper, we propose a novel color-texture image segmentation method based on local histogra... more In this paper, we propose a novel color-texture image segmentation method based on local histograms. Starting with clustering-based color quantization, we extract a sufficient number of representative colors. For each pixel, through counting the number of pixels with each representative color within a circular neighborhood, a local histogram is obtained. After the circular neighborhood is extended to several scales, a local histogram with an appropriate scale is adopted as a color-texture descriptor at the corresponding pixel for image segmentation. Further, we correct the color-texture features near boundaries and obtain a initial segmentation by a clustering method with the color-texture descriptors. Finally, in order to obtain a better segmentation result, we merge the over segmented regions guided by the obtained boundaries. Experiments are performed on both synthetic and natural color-texture images, and the results show that our proposed method performs much better compared with state-of-the-art methods on image segmentation, particularly in textured areas.

IEEE Transactions on Image Processing, 2019

Image corner detection is very important in the fields of image analysis and computer vision. Cur... more Image corner detection is very important in the fields of image analysis and computer vision. Curvature calculation techniques are used in many contour-based corner detectors. We identify that existing calculation of curvature is sensitive to local variation and noise in the discrete domain and does not perform well when corners are closely located. In this paper, discrete curvature representations of single and double corner models are investigated and obtained. A number of model properties have been discovered which help us detect corners on contours. It is shown that the proposed method has a high corner resolution (the ability to accurately detect neighbouring corners) and a corresponding corner resolution constant is also derived. Meanwhile, this method is less sensitive to any local variations and noise on the contour; and false corner detection is less likely to occur. The proposed detector is compared with seven state-of-the-art detectors. Three test images with ground truths are used to assess the detection capability and localization accuracy of these methods in noise-free and cases with different noise levels. Twenty-four images with various scenes without ground truths are used to evaluate their repeatability under affine transformation, JPEG compression, and noise degradations. The experimental results show that our proposed detector attains a better overall performance.

2014 International Conference on Digital Image Computing: Techniques and Applications (DICTA), 2014

An approach is suggested for automating fish identification and measurement using stereo Baited R... more An approach is suggested for automating fish identification and measurement using stereo Baited Remote Underwater Video footage. Simple methods for identifying fish are not sufficient for measurement, since the snout and tail points must be found, and the stereo data should be incorporated to find a true measurement. We present a modular framework that ties together various approaches in order to develop a generalised system for automated fish detection. A method is also suggested for using machine learning to improve identification. Experimental results indicate the suitability of our approach.

Procedings of the British Machine Vision Conference 2004, 2004

The application of energy minimisation methods for stereo matching has been demonstrated to produ... more The application of energy minimisation methods for stereo matching has been demonstrated to produce high quality disparity maps. However the majority of these methods are known to be computationally expensive, requiring minutes or even hours of computation. We propose a fast minimisation scheme that produces strongly competitive results for significantly reduced computation, requiring only a few seconds of computation. In this paper, we present our iterated dynamic programming algorithm along with a quadtree subregioning process for fast stereo matching.

International Journal of Computer Vision, 2002

This paper presents a fast and reliable stereo matching algorithm which produces a dense disparit... more This paper presents a fast and reliable stereo matching algorithm which produces a dense disparity map by using fast cross correlation, rectangular subregioning (RSR) and 3D maximum-surface techniques in a coarse-to-fine scheme. Fast correlation is achieved by using the box-filtering technique whose speed is invariant to the size of the correlation window and by segmenting the stereo images into rectangular subimages at different levels of the pyramid. By working with rectangular subimages, not only can the speed of the correlation be further increased, the intermediate memory storage requirement can also be reduced. The disparity map for the stereo images is found in the 3D correlation coefficient volume by obtaining the global 3D maximum-surface rather than simply choosing the position that gives the local maximum correlation coefficient value for each pixel. The 3D maximum-surface is obtained using our new two-stage dynamic programming (TSDP) technique. There are two original contributions in this paper: (1) development of the RSR technique for fast similarity measure; and (2) development of the TSDP technique for efficiently obtaining 3D maximum-surface in a 3D volume. Typical running time of our algorithm implemented in the C language on a 512 × 512 image is in the order of a few seconds on a 500 MHz PC. A variety of synthetic and real images have been tested, and good results have been obtained.

Advances in experimental medicine and biology, 2015

This chapter describes a novel way of carrying out image analysis, reconstruction and processing ... more This chapter describes a novel way of carrying out image analysis, reconstruction and processing tasks using cloud based service provided on the Australian National eResearch Collaboration Tools and Resources (NeCTAR) infrastructure. The toolbox allows users free access to a wide range of useful blocks of functionalities (imaging functions) that can be connected together in workflows allowing creation of even more complex algorithms that can be re-run on different data sets, shared with others or additionally adjusted. The functions given are in the area of cellular imaging, advanced X-ray image analysis, computed tomography and 3D medical imaging and visualisation. The service is currently available on the website www.cloudimaging.net.au .

2010 International Conference on Digital Image Computing: Techniques and Applications, 2010

Signal Processing: Image Communication, 2014

ABSTRACT Segment based disparity estimation methods have been proposed in many different ways. Mo... more ABSTRACT Segment based disparity estimation methods have been proposed in many different ways. Most of these studies are built upon the hypothesis that no large disparity jump exists within a segment. When this hypothesis does not hold true, it is difficult for these methods to estimate disparities correctly. Therefore, these methods work well only when the images are initially over segmented but do not work well for under segmented cases. To solve this problem, we present a new segment based stereo matching method which consists of two algorithms: a cost volume watershed algorithm (CVW) and a region merging (RM) algorithm. For incorrectly under segmented regions where pixels on different objects are grouped into one segment, the CVW algorithm regroups the pixels on different objects into different segments and provides disparity estimation to the pixels in different segments accordingly. For unreliable and occluded regions, we merge them into neighboring reliable segments for robust disparity estimation. The comparison between our method and the current state-of-the-art methods shows that our method is very competitive and is robust particularly when the images are initially under segmented.

Proceedings of the 27th Conference on Image and Vision Computing New Zealand - IVCNZ '12, 2012

ABSTRACT We present a new method for dense stereo matching based on a tree structural cost volume... more ABSTRACT We present a new method for dense stereo matching based on a tree structural cost volume watershed (TSCVW) and a region combination (RC) process. Given a cost volume as the data cost and an initial segmentation result, the proposed TSCVW method reliably estimates the disparities in a segment by using energy optimization to control plane segmentation and plane fitting. Then the disparities in the incorrectly fitted and occluded regions are refined using our RC process. Experimental results show that our method is very robust to different initial segmentation results and the shape of a segment. The comparison between our algorithm and the current state-of-the-art algorithms on the Middlebury website shows that our algorithm is very competitive.

2012 International Conference on Digital Image Computing Techniques and Applications (DICTA), 2012

ABSTRACT This paper presents a new method for finding feature correspondences between a pair of s... more ABSTRACT This paper presents a new method for finding feature correspondences between a pair of stereo images, which can be used to perform 3D reconstruction and object recognition. This paper uses epiploar geometry to determine the location of potential matching points which allow the finding of the correspondences faster and more accurately. An adaptive smoothness algorithm is also proposed to filter out false matches based on the disparity jump in neighboring correspondences. More correspondences are then identified in such a way that they are evenly distributed in the images. Experimental results show that the proposed method effectively improve the percentage of correct matches, total number of correct matches, and even distribution of the correspondences.

Computer Science & Information Technology ( CS & IT ), 2014

Organ segmentation from medical images is still an open problem and liver segmentation is a much ... more Organ segmentation from medical images is still an open problem and liver segmentation is a much more challenging task among other organ segmentations. This paper presents a liver segmentation method from a sequence of computer to mography images.We propose a novel balloon force that controls the direction of the evolution process and slows down the evolving contour in regions with weak or without edges and discourages the evolving contour from going far away from the liver boundary or from leaking at a region that has a weak edge, or does not have an edge. The model is implemented using a modified Distance Regularized Level Set (DRLS) model. The experimental results show that the method can achieve a satisfactory result. Comparing with the original DRLS model, our model is more effective in dealing with over segmentation problems.

Computer Science & Information Technology ( CS & IT ), 2014

In this paper, we propose a novel global threshold-based active contour model which employs a new... more In this paper, we propose a novel global threshold-based active contour model which employs a new edge-stopping function that controls the direction of the evolution and stops the evolving contour at weak or blurred edges. The model is implemented using selective binary and Gaussian filtering regularized level set (SBGFRLS) method. The method has a selective local or global segmentation property. It selectively penalizes the level set function to be a binary function. This is followed by using a Gaussian function to regularize it. The Gaussian filters smooth the level set function and afford the evolution more stability. The contour could be initialized anywhere inside the image to extract object boundaries. The proposed method performs well when the intensities inside and outside the object are homogenous. Our method is tested on synthetic, medical and Arabiccharacters images with satisfactory results

Image and Vision Computing, 2008

The application of energy minimisation methods for stereo matching has been demonstrated to produ... more The application of energy minimisation methods for stereo matching has been demonstrated to produce high quality disparity maps. However, the majority of these methods are known to be computationally expensive requiring minutes of computation. In this paper, we propose a fast minimisation scheme that produces high quality stereo reconstructions for significantly reduced running time, requiring only a few seconds of computation. The minimisation scheme is carried out using our iterated dynamic programming algorithm, which iterates over entire rows and columns for fast stereo matching. A quadtree subregioning process is also used for efficient computation of a matching cost volume where iterated dynamic programming operates on.

Image and Vision Computing, 2002

Optical flow or image motion estimation is important in the area of computer vision. This paper p... more Optical flow or image motion estimation is important in the area of computer vision. This paper presents a fast and reliable optical flow algorithm which produces a dense optical flow map by using fast cross correlation and 3D shortest path techniques. Fast correlation is achieved by using the box-filtering technique which is invariant to the size of the correlation window. The motion for each scanline or each column of the input image is obtained from the correlation coefficient volume by finding the best 3D path using dynamic programming techniques rather than simply choosing the position that gives the maximum cross correlation coefficient. Sub-pixel accuracy is achieved by fitting the local correlation coefficients to a quadratic surface. Typical running time for a 256 £ 256 image is in the order of a few seconds on a 85 MHz computer. A variety of synthetic and real images have been tested, and good results have been obtained.

IEEE Transactions on Medical Imaging, 2014

This paper presents the evaluation results of the methods submitted to Challenge US: Biometric Me... more This paper presents the evaluation results of the methods submitted to Challenge US: Biometric Measurements from Fetal Ultrasound Images, a segmentation challenge held at the IEEE International Symposium on Biomedical Imaging 2012. The challenge was set to compare and evaluate current fetal ultrasound image segmentation methods. It consisted of automatically segmenting fetal anatomical structures to measure standard obstetric biometric parameters, from 2D fetal ultrasound images taken on fetuses at different gestational ages (21 weeks, 28 weeks, and 33 weeks) and with varying image quality to reflect data encountered in real clinical environments. Four independent sub-challenges were proposed, according to the objects of interest measured in clinical practice: abdomen, head, femur, and whole fetus. Five teams participated in the head sub-challenge and two teams in the femur sub-challenge, including one team who tackled both. Nobody attempted the abdomen and whole fetus

IEEE Transactions on Consumer Electronics, 2001

This paper presents a fast algorithm for de-interlacing of video images using a shortest path tec... more This paper presents a fast algorithm for de-interlacing of video images using a shortest path technique. The algorithm applies dynamic programming techniques to find a shortest path in a cost matrix. The motion information obtained from this shortest path is used to realign the fields of a video image. By using the shortest path via dynamic programming, the motion information estimated is more reliable than simply performing a search in a local neighbourhood. A variety of real images have been tested, and good results have been obtained.

IEEE Transactions on Pattern Analysis and Machine Intelligence

Interest point detection is one of the most fundamental and critical problems in computer vision ... more Interest point detection is one of the most fundamental and critical problems in computer vision and image processing. In this paper, we carry out a comprehensive review on image feature information (IFI) extraction techniques for interest point detection. To systematically introduce how the existing interest point detection methods extract IFI from an input image, we propose a taxonomy of the IFI extraction techniques for interest point detection. According to this taxonomy, we discuss different types of IFI extraction techniques for interest point detection. Furthermore, we identify the main unresolved issues related to the existing IFI extraction techniques for interest point detection and any interest point detection methods that have not been discussed before. The existing popular datasets and evaluation standards are provided and the performances for eighteen state-of-the-art approaches are evaluated and discussed. Moreover, future research directions on IFI extraction techniques for interest point detection are elaborated.

IEEE Access, 2019

In this paper, we propose a novel color-texture image segmentation method based on local histogra... more In this paper, we propose a novel color-texture image segmentation method based on local histograms. Starting with clustering-based color quantization, we extract a sufficient number of representative colors. For each pixel, through counting the number of pixels with each representative color within a circular neighborhood, a local histogram is obtained. After the circular neighborhood is extended to several scales, a local histogram with an appropriate scale is adopted as a color-texture descriptor at the corresponding pixel for image segmentation. Further, we correct the color-texture features near boundaries and obtain a initial segmentation by a clustering method with the color-texture descriptors. Finally, in order to obtain a better segmentation result, we merge the over segmented regions guided by the obtained boundaries. Experiments are performed on both synthetic and natural color-texture images, and the results show that our proposed method performs much better compared with state-of-the-art methods on image segmentation, particularly in textured areas.

IEEE Transactions on Image Processing, 2019

Image corner detection is very important in the fields of image analysis and computer vision. Cur... more Image corner detection is very important in the fields of image analysis and computer vision. Curvature calculation techniques are used in many contour-based corner detectors. We identify that existing calculation of curvature is sensitive to local variation and noise in the discrete domain and does not perform well when corners are closely located. In this paper, discrete curvature representations of single and double corner models are investigated and obtained. A number of model properties have been discovered which help us detect corners on contours. It is shown that the proposed method has a high corner resolution (the ability to accurately detect neighbouring corners) and a corresponding corner resolution constant is also derived. Meanwhile, this method is less sensitive to any local variations and noise on the contour; and false corner detection is less likely to occur. The proposed detector is compared with seven state-of-the-art detectors. Three test images with ground truths are used to assess the detection capability and localization accuracy of these methods in noise-free and cases with different noise levels. Twenty-four images with various scenes without ground truths are used to evaluate their repeatability under affine transformation, JPEG compression, and noise degradations. The experimental results show that our proposed detector attains a better overall performance.

2014 International Conference on Digital Image Computing: Techniques and Applications (DICTA), 2014

An approach is suggested for automating fish identification and measurement using stereo Baited R... more An approach is suggested for automating fish identification and measurement using stereo Baited Remote Underwater Video footage. Simple methods for identifying fish are not sufficient for measurement, since the snout and tail points must be found, and the stereo data should be incorporated to find a true measurement. We present a modular framework that ties together various approaches in order to develop a generalised system for automated fish detection. A method is also suggested for using machine learning to improve identification. Experimental results indicate the suitability of our approach.

Procedings of the British Machine Vision Conference 2004, 2004

The application of energy minimisation methods for stereo matching has been demonstrated to produ... more The application of energy minimisation methods for stereo matching has been demonstrated to produce high quality disparity maps. However the majority of these methods are known to be computationally expensive, requiring minutes or even hours of computation. We propose a fast minimisation scheme that produces strongly competitive results for significantly reduced computation, requiring only a few seconds of computation. In this paper, we present our iterated dynamic programming algorithm along with a quadtree subregioning process for fast stereo matching.

International Journal of Computer Vision, 2002

This paper presents a fast and reliable stereo matching algorithm which produces a dense disparit... more This paper presents a fast and reliable stereo matching algorithm which produces a dense disparity map by using fast cross correlation, rectangular subregioning (RSR) and 3D maximum-surface techniques in a coarse-to-fine scheme. Fast correlation is achieved by using the box-filtering technique whose speed is invariant to the size of the correlation window and by segmenting the stereo images into rectangular subimages at different levels of the pyramid. By working with rectangular subimages, not only can the speed of the correlation be further increased, the intermediate memory storage requirement can also be reduced. The disparity map for the stereo images is found in the 3D correlation coefficient volume by obtaining the global 3D maximum-surface rather than simply choosing the position that gives the local maximum correlation coefficient value for each pixel. The 3D maximum-surface is obtained using our new two-stage dynamic programming (TSDP) technique. There are two original contributions in this paper: (1) development of the RSR technique for fast similarity measure; and (2) development of the TSDP technique for efficiently obtaining 3D maximum-surface in a 3D volume. Typical running time of our algorithm implemented in the C language on a 512 × 512 image is in the order of a few seconds on a 500 MHz PC. A variety of synthetic and real images have been tested, and good results have been obtained.

Advances in experimental medicine and biology, 2015

This chapter describes a novel way of carrying out image analysis, reconstruction and processing ... more This chapter describes a novel way of carrying out image analysis, reconstruction and processing tasks using cloud based service provided on the Australian National eResearch Collaboration Tools and Resources (NeCTAR) infrastructure. The toolbox allows users free access to a wide range of useful blocks of functionalities (imaging functions) that can be connected together in workflows allowing creation of even more complex algorithms that can be re-run on different data sets, shared with others or additionally adjusted. The functions given are in the area of cellular imaging, advanced X-ray image analysis, computed tomography and 3D medical imaging and visualisation. The service is currently available on the website www.cloudimaging.net.au .

2010 International Conference on Digital Image Computing: Techniques and Applications, 2010

Signal Processing: Image Communication, 2014

ABSTRACT Segment based disparity estimation methods have been proposed in many different ways. Mo... more ABSTRACT Segment based disparity estimation methods have been proposed in many different ways. Most of these studies are built upon the hypothesis that no large disparity jump exists within a segment. When this hypothesis does not hold true, it is difficult for these methods to estimate disparities correctly. Therefore, these methods work well only when the images are initially over segmented but do not work well for under segmented cases. To solve this problem, we present a new segment based stereo matching method which consists of two algorithms: a cost volume watershed algorithm (CVW) and a region merging (RM) algorithm. For incorrectly under segmented regions where pixels on different objects are grouped into one segment, the CVW algorithm regroups the pixels on different objects into different segments and provides disparity estimation to the pixels in different segments accordingly. For unreliable and occluded regions, we merge them into neighboring reliable segments for robust disparity estimation. The comparison between our method and the current state-of-the-art methods shows that our method is very competitive and is robust particularly when the images are initially under segmented.

Proceedings of the 27th Conference on Image and Vision Computing New Zealand - IVCNZ '12, 2012

ABSTRACT We present a new method for dense stereo matching based on a tree structural cost volume... more ABSTRACT We present a new method for dense stereo matching based on a tree structural cost volume watershed (TSCVW) and a region combination (RC) process. Given a cost volume as the data cost and an initial segmentation result, the proposed TSCVW method reliably estimates the disparities in a segment by using energy optimization to control plane segmentation and plane fitting. Then the disparities in the incorrectly fitted and occluded regions are refined using our RC process. Experimental results show that our method is very robust to different initial segmentation results and the shape of a segment. The comparison between our algorithm and the current state-of-the-art algorithms on the Middlebury website shows that our algorithm is very competitive.

2012 International Conference on Digital Image Computing Techniques and Applications (DICTA), 2012

ABSTRACT This paper presents a new method for finding feature correspondences between a pair of s... more ABSTRACT This paper presents a new method for finding feature correspondences between a pair of stereo images, which can be used to perform 3D reconstruction and object recognition. This paper uses epiploar geometry to determine the location of potential matching points which allow the finding of the correspondences faster and more accurately. An adaptive smoothness algorithm is also proposed to filter out false matches based on the disparity jump in neighboring correspondences. More correspondences are then identified in such a way that they are evenly distributed in the images. Experimental results show that the proposed method effectively improve the percentage of correct matches, total number of correct matches, and even distribution of the correspondences.

Computer Science & Information Technology ( CS & IT ), 2014

Organ segmentation from medical images is still an open problem and liver segmentation is a much ... more Organ segmentation from medical images is still an open problem and liver segmentation is a much more challenging task among other organ segmentations. This paper presents a liver segmentation method from a sequence of computer to mography images.We propose a novel balloon force that controls the direction of the evolution process and slows down the evolving contour in regions with weak or without edges and discourages the evolving contour from going far away from the liver boundary or from leaking at a region that has a weak edge, or does not have an edge. The model is implemented using a modified Distance Regularized Level Set (DRLS) model. The experimental results show that the method can achieve a satisfactory result. Comparing with the original DRLS model, our model is more effective in dealing with over segmentation problems.

Computer Science & Information Technology ( CS & IT ), 2014

In this paper, we propose a novel global threshold-based active contour model which employs a new... more In this paper, we propose a novel global threshold-based active contour model which employs a new edge-stopping function that controls the direction of the evolution and stops the evolving contour at weak or blurred edges. The model is implemented using selective binary and Gaussian filtering regularized level set (SBGFRLS) method. The method has a selective local or global segmentation property. It selectively penalizes the level set function to be a binary function. This is followed by using a Gaussian function to regularize it. The Gaussian filters smooth the level set function and afford the evolution more stability. The contour could be initialized anywhere inside the image to extract object boundaries. The proposed method performs well when the intensities inside and outside the object are homogenous. Our method is tested on synthetic, medical and Arabiccharacters images with satisfactory results

Image and Vision Computing, 2008

The application of energy minimisation methods for stereo matching has been demonstrated to produ... more The application of energy minimisation methods for stereo matching has been demonstrated to produce high quality disparity maps. However, the majority of these methods are known to be computationally expensive requiring minutes of computation. In this paper, we propose a fast minimisation scheme that produces high quality stereo reconstructions for significantly reduced running time, requiring only a few seconds of computation. The minimisation scheme is carried out using our iterated dynamic programming algorithm, which iterates over entire rows and columns for fast stereo matching. A quadtree subregioning process is also used for efficient computation of a matching cost volume where iterated dynamic programming operates on.

Image and Vision Computing, 2002

Optical flow or image motion estimation is important in the area of computer vision. This paper p... more Optical flow or image motion estimation is important in the area of computer vision. This paper presents a fast and reliable optical flow algorithm which produces a dense optical flow map by using fast cross correlation and 3D shortest path techniques. Fast correlation is achieved by using the box-filtering technique which is invariant to the size of the correlation window. The motion for each scanline or each column of the input image is obtained from the correlation coefficient volume by finding the best 3D path using dynamic programming techniques rather than simply choosing the position that gives the maximum cross correlation coefficient. Sub-pixel accuracy is achieved by fitting the local correlation coefficients to a quadratic surface. Typical running time for a 256 £ 256 image is in the order of a few seconds on a 85 MHz computer. A variety of synthetic and real images have been tested, and good results have been obtained.

IEEE Transactions on Medical Imaging, 2014

This paper presents the evaluation results of the methods submitted to Challenge US: Biometric Me... more This paper presents the evaluation results of the methods submitted to Challenge US: Biometric Measurements from Fetal Ultrasound Images, a segmentation challenge held at the IEEE International Symposium on Biomedical Imaging 2012. The challenge was set to compare and evaluate current fetal ultrasound image segmentation methods. It consisted of automatically segmenting fetal anatomical structures to measure standard obstetric biometric parameters, from 2D fetal ultrasound images taken on fetuses at different gestational ages (21 weeks, 28 weeks, and 33 weeks) and with varying image quality to reflect data encountered in real clinical environments. Four independent sub-challenges were proposed, according to the objects of interest measured in clinical practice: abdomen, head, femur, and whole fetus. Five teams participated in the head sub-challenge and two teams in the femur sub-challenge, including one team who tackled both. Nobody attempted the abdomen and whole fetus

IEEE Transactions on Consumer Electronics, 2001

This paper presents a fast algorithm for de-interlacing of video images using a shortest path tec... more This paper presents a fast algorithm for de-interlacing of video images using a shortest path technique. The algorithm applies dynamic programming techniques to find a shortest path in a cost matrix. The motion information obtained from this shortest path is used to realign the fields of a video image. By using the shortest path via dynamic programming, the motion information estimated is more reliable than simply performing a search in a local neighbourhood. A variety of real images have been tested, and good results have been obtained.