Ncut Method Research Articles

A Variational Image Segmentation Model Based on Normalized Cut with Adaptive Similarity and Spatial Regularization

Image segmentation is a fundamental research topic in image processing and computer vision. In recent decades, researchers developed a large number of segmentation algorithms for various applications. Among these algorithms, the normalized cut (Ncut) segmentation method is widely applied due to its good performance. The Ncut segmentation model is an optimization problem whose energy is defined on a specifically designed graph. Thus, the segmentation results of the existing Ncut method are largely dependent on a preconstructed similarity measure on the graph since this measure is usually given empirically by users. This flaw will lead to some undesirable segmentation results. In this paper, we propose an Ncut-based segmentation algorithm by integrating an adaptive similarity measure and spatial regularization. The proposed model combines the Parzen--Rosenblatt window method, nonlocal weights entropy, Ncut energy, and regularizer of phase field in a variational framework. Our method can adaptively update the similarity measure function by estimating some parameters. This adaptive procedure enables the proposed algorithm to find a better similarity measure for classification than the Ncut method. We provide some mathematical interpretation of the proposed adaptive similarity from multiple viewpoints, such as statistics and convex optimization. In addition, the regularizer of phase field can guarantee that the proposed algorithm has a robust performance in the presence of noise, and it can also rectify the similarity measure with a spatial priori. The well-posed theory such as the existence of the minimizer for the proposed model is given in the paper. Compared with some existing segmentation methods such as the traditional Ncut-based model and the classical Chan--Vese model, the numerical experiments show that our method can provide promising segmentation results.

Novel Image Segmentation Methods Based on Improved Ncut Algorithm

Image segmentation is an important process from image processing to image analysis and scene understanding. Targets of different scales in an image may belong to different classes. Single scale image segmentation methods are prone to over-segmentation or under-segmentation. Combining MeanShfit and Ncut multiscale sampling image segmentation methods, the image is smoothed by MeanShift algorithm and the edges are preserved. Clustering using weights (similarities) between two pixels by Ncut method, this method can be applied to remote sensing image segmentation. In order to solve the problems of high time complexity and long calculation time of Ncut algorithm, firstly, the entropy rate superpixel segmentation algorithm is used to over-segment the image. The algorithm divides the image into a series of compact regions with good regional consistency, Combining Ncut method to solve the weights of similarity between two superpixels to determine the attribution of the region can reduce the segmentation time. Experiments show that this method can use multiscale information for image segmentation effectively. The first method can be applied to remote sensing image segmentation, and the second method can improve the efficiency of Ncut which is suitable for natural scene image segmentation.

Fast Segmentation of Colour Apple Image under All-Weather Natural Conditions for Vision Recognition of Picking Robots

In order to resolve the poor real-time performance problem of the normalized cut (Ncut) method in apple vision recognition of picking robots, a fast segmentation method of colour apple images based on the adaptive mean-shift and Ncut methods is proposed in this paper. Firstly, the traditional Ncut method based on pixels is changed into the Ncut method based on regions by the adaptive mean-shift initial segmenting. In this way, the number of peaks and edges in the image is dramatically reduced and the computation speed is improved. Secondly, the image is divided into regional maps by extracting the R-B colour feature, which not only reduces the quantity of regions, but also to some extent overcomes the effect on illumination. On this basis, every region map is expressed by a region point, so the undirected graph of the R-B colour grey-level feature is attained. Finally, regarding the undirected graph as the input of Ncut, we construct the weight matrix W by region points and determine the number of clusters based on the decision-theoretic rough set. The adaptive clustering segmentation can be implemented by an Ncut algorithm. Experimental results show that the maximum segmentation error is 3% and the average recognition time is less than 0.7s, which can meet the requirements of a real-time picking robot.

Iterative ensemble normalized cuts

A fast spectral clustering method is proposed. Eigenvectors used in NCut are studied as the gap-normalized distances defined in this paper. The out-of-sample extensions of NCut are derived by extending the gap-normalized distances to new data, which is interestingly found to be perfectly matched with the Nyström-based eigenfunction approximation. From the view of gap-normalized distance, the ensemble NCut method is built by assembling distances of small groups to learn the partitions of the entire dataset. By iteratively calling such assembly, the iterative ensemble NCut method is proposed. Experiments on real world datasets and the image segmentation tasks show that, compared with the state-of-the-art, the proposed IENCut method produces improved clustering quality although this improvement may sometimes come at the expense of increased processing time.

Using Tree Detection Algorithms to Predict Stand Sapwood Area, Basal Area and Stocking Density in Eucalyptus regnans Forest

Managers of forested water supply catchments require efficient and accurate methods to quantify changes in forest water use due to changes in forest structure and density after disturbance. Using Light Detection and Ranging (LiDAR) data with as few as 0.9 pulses m−2, we applied a local maximum filtering (LMF) method and normalised cut (NCut) algorithm to predict stocking density (SDen) of a 69-year-old Eucalyptus regnans forest comprising 251 plots with resolution of the order of 0.04 ha. Using the NCut method we predicted basal area (BAHa) per hectare and sapwood area (SAHa) per hectare, a well-established proxy for transpiration. Sapwood area was also indirectly estimated with allometric relationships dependent on LiDAR derived SDen and BAHa using a computationally efficient procedure. The individual tree detection (ITD) rates for the LMF and NCut methods respectively had 72% and 68% of stems correctly identified, 25% and 20% of stems missed, and 2% and 12% of stems over-segmented. The significantly higher computational requirement of the NCut algorithm makes the LMF method more suitable for predicting SDen across large forested areas. Using NCut derived ITD segments, observed versus predicted stand BAHa had R2 ranging from 0.70 to 0.98 across six catchments, whereas a generalised parsimonious model applied to all sites used the portion of hits greater than 37 m in height (PH37) to explain 68% of BAHa. For extrapolating one ha resolution SAHa estimates across large forested catchments, we found that directly relating SAHa to NCut derived LiDAR indices (R2 = 0.56) was slightly more accurate but computationally more demanding than indirect estimates of SAHa using allometric relationships consisting of BAHa (R2 = 0.50) or a sapwood perimeter index, defined as (BAHaSDen)½ (R2 = 0.48).

Genetic cuts for image segmentation

The normalized cut (Ncut) method is a popular method for segmenting images and videos. The Ncut method segments an image into two disjoint regions, each segmented by the same method. After the Ncut method has been recursively applied to an image, its final segmented image is obtained. The main drawback of the Ncut method is that a user cannot easily determine the stop criteria because users have no idea about the number of regions in an image. This work proposes the genetic cut (Gcut) algorithm to resolve this shortcoming. Users do need not to specify thresholds in the Gcut algorithm, which automatically segments an image into the proper number of regions. Also, the neighbor-merging (NM) algorithm is proposed for preprocessing the images and improves the performance of the Gcut algorithm. Thus, the proposed Gcut method combines the NM and Gcut algorithms. Furthermore, a heuristic method is proposed to identify a good segment for the Gcut method. In all experiments, the proposed Gcut method outperforms traditional Ncut methods.

Automated detection of the arterial input function using normalized cut clustering to determine cerebral perfusion by dynamic susceptibility contrast-magnetic resonance imaging.

To propose a new clustering method for the automatic detection of arterial input function (AIF) with high accuracy in dynamic susceptibility contrast-magnetic resonance imaging (DSC-MRI). A novel method for automatically determining the AIF was proposed to facilitate the analysis of MR perfusion, which relied on normalized cut (Ncut) clustering. Its performance was compared with those of two other previously reported clustering methods: k-means and fuzzy c-means (FCM) techniques, in terms of the detection accuracy and computational time. Both simulated perfusion data and data collected from 42 healthy human subjects were applied to investigate the feasibility of the proposed approach. In the simulation study, the partial volume effect (PVE) level, peak value (PV), time to peak (TTP), full width at half maximum (FWHM), area under AIF curve (AUC), root mean square error (RMSE) between the estimated AIF and true AIF, and M value given by [PV/(FWHM×TTP)] were 45.45, 4.2737, 29.92, 6.4563, 76.4836, 0.0519, and 0.0221 for Ncut-based AIF, 96.45, 3.8385, 31.74, 7.5133, 75.7364, 0.3295, and 0.0161 for FCM-based AIF, 91.18, 3.8990, 31.73, 7.4544, 76.0476, 0.3128, and 0.0165 for k-means-based AIF, 0, 4.4592, 29.51, 6.2016, 76.8669, 0, and 0.0244 for true AIF. In the clinical study, the mean PV, TTP, FWHM, AUC, M, error between estimated AIF and manual AIF were 1.7395, 30.95, 5.5923, 19.1081, 0.0397, and 0.4406 for Ncut-based AIF, 1.3629, 31.31, 6.8616, 17.9992, 0.0123, and 0.0846 for k-means-based AIF, 1.2101, 31.61, 7.1729, 16.6238, 0.0102, and 0.1016 for FCM-based AIF. The differences in PV, M, FWHM, and error reached a significant level (P = 0.032, 0.010, 0.003, and 0.002, respectively) between Ncut and k-means methods as well as between Ncut and FCM methods (P = 0.013, 0.008, 0.007, and 0.009, respectively). There was no significant difference in TTP between Ncut and each of the other two methods (P = 0.173 and 0.097, respectively). For AUC, a significant difference was found between Ncut and FCM algorithms (P = 0.025), but not between Ncut and k-means methods (P = 0.138). The mean execution time was 0.4406 for the Ncut method, 0.2649 for the k-means method, and 0.1371 for the FCM method, and the differences were significant both between Ncut and k-means methods (P = 0.002) and between Ncut and FCM methods (P = 0.004). Ncut clustering yield AIFs more in line with the expected AIF, and might be preferred to FCM and k-means clustering methods sensitive to randomly selected initial centers.

Automatic extraction of feather quill based on Normalized cut algorithm

A modified Normalized cut(Ncut) method considering the texture weight was proposed to effectively segment feather quill.The weight including texture information enhanced association on each edge of similar texture and reduced interference of the similar region.Narrow unidirectional expansion method with a region-scalable fitting term was used to optimize the initial boundary for the final result and eliminated boundary leakage of the feather quill.The experimental results show that the proposed method can realize boundary extraction of feather quill efficiently and pave the way for the next step research of crease detection.

Segmentation of tumor ultrasound image via region-based Ncut method

To segment the tumor region precisely is a prerequisite for ultrasound navigation and treatment. In this paper, a normalized cut method to segment tumor ultrasound image is proposed by means of simple linear iterative clustering for pre-segmentation procedure. The first step, we use simple linear iterative clustering algorithm to divide the image into a number of homogeneous over-segmented regions. Then, these regions are regarded as nodes, and a similarity matrix is constructed by comparing the histograms of each two regions. Finally, we apply the Ncut method to merging the over-segmented regions, then the image segmentation process is completed. The results show that the proposed segmentation scheme handles the strong speckle noise, low contrast, and weak edges well in ultrasound image. Our method has high segmentation precision and computation efficiency than the pixel-based Ncut method.

Color Image Segmentation Based on Mean Shift and Normalized Cuts

In this correspondence, we develop a novel approach that provides effective and robust segmentation of color images. By incorporating the advantages of the mean shift (MS) segmentation and the normalized cut (Ncut) partitioning methods, the proposed method requires low computational complexity and is therefore very feasible for real-time image segmentation processing. It preprocesses an image by using the MS algorithm to form segmented regions that preserve the desirable discontinuity characteristics of the image. The segmented regions are then represented by using the graph structures, and the Ncut method is applied to perform globally optimized clustering. Because the number of the segmented regions is much smaller than that of the image pixels, the proposed method allows a low-dimensional image clustering with significant reduction of the complexity compared to conventional graph-partitioning methods that are directly applied to the image pixels. In addition, the image clustering using the segmented regions, instead of the image pixels, also reduces the sensitivity to noise and results in enhanced image segmentation performance. Furthermore, to avoid some inappropriate partitioning when considering every region as only one graph node, we develop an improved segmentation strategy using multiple child nodes for each region. The superiority of the proposed method is examined and demonstrated through a large number of experiments using color natural scene images.

Image segmentation by unsupervised sparse clustering

In this paper, we present a novel solution for image segmentation based on positiveness which regards the segmentation as a graph-theoretic clustering problem. Contrary to spectral clustering methods using eigenvectors, the proposed method tries to find an additive combination of positive components from an originally positive data-driven matrix. By using the positiveness constraint, we obtain sparsely clustered results which do not include cancellations by negative entries. Thus, we call this method sparse clustering. The proposed method adopts a binary tree structure and solves a model selection problem by automatically determining the number of clusters using intra- and inter-cluster measures. We tested our method with image sequences as well as single frame data such as points and gray-scale, color, and texture images. Moreover, in order to objectively evaluate the performance of our method, we compared the results of the proposed method with those of the human segmentation and the Ncut method using various images including the Berkeley datasets. Experimental results show that the proposed method provides very successful and encouraging segmentations.