Citation Context

... an objective function that expresses the quality of the decomposition (i.e.,the index of cluster validity). The objective function typically compares the inter- versus intra-cluster variability [30],=-=[28]-=- or evaluates the isolation and connectivity of the delineated clusters [43]. . Finally,since in most of the cases the decomposition is task dependent,top-down information provided by the user or by a...

Citation Context

...mizes an objective function that expresses the quality of the decomposition (i.e.,the index of cluster validity). The objective function typically compares the inter- versus intra-cluster variability =-=[30]-=-,[28] or evaluates the isolation and connectivity of the delineated clusters [43]. . Finally,since in most of the cases the decomposition is task dependent,top-down information provided by the user or...

Citation Context

...4c. The segmentation step does not add a significant overhead to the filtering process. The region representation used by the mean shift segmentation is similar to the blob representation employed in =-=[64]-=-. However, while the blob has a parametric description (multivariate Gaussians in both spatial and color domain), the partition generated by the mean shift is characterized by a nonparametric model. A...

Citation Context

... already discusses a simple example. However,by introducing adequate objective functions,the optimization problem can acquire physical meaning in the context of a computer vision task. For example,in =-=[14]-=-,by defining the distance between the distributions of the model and a candidate of the target,nonrigid objects were tracked in an image sequence under severe distortions. The distance was defined at ...

Citation Context

...eature space [25, 60, 63]. Our approach to mode detection and clustering is based on the mean shift procedure, proposed in 1975 by Fukunaga and Hostetler [21] and largely forgotten till Cheng’s paper =-=[7]-=- rekindled the interest in it. In spite of its excellent qualities, the mean shift procedure does not seem to be known in the statistical literature. While the book [54, Sec.6.2.2] discusses [21], the...

Citation Context

...ametric toolbox developed in this paper is suitable for a large variety of computer vision tasks where parametric models are less adequate, for example, modeling the background in visual surveillance =-=[18]-=-. The complete solution toward autonomous image segmentation is to combine a bandwidth selection technique (like the ones discussed in Section 3.1) with top-down task related high level information. I...

Citation Context

...ineated based on the local structure of the feature space [25],[60],[63]. Our approach to mode detection and clustering is based on the mean shift procedure,proposed in 1975 by Fukunaga and Hostetler =-=[21]-=- and largely forgotten until Cheng's paper [7] rekindled interest in it. In spite of its excellent qualities,the mean shift procedure does not seem to be known in statistical literature. While the boo...

Citation Context

...stopping criterion and after a sufficiently large number of iterations, the processed image collapses into a flat surface. The connection between anisotropic diffusion and M-estimators is analyzed in =-=[5]-=-. A recently proposed noniterative discontinuity preserving smoothing technique is the bilateral filtering [59]. The relation between bilateral filtering and diffusion based techniques was analyzed in...

Citation Context

...s on the Laplacian of the unknown density being estimated,and its performance is not well understood [62,p. 108]. For the univariate case,a reliable method for bandwidth selection is the plug-in rule =-=[53]-=-,which was proven to be superior to leastsquares cross-validation and biased cross-validation [42],[55,p. 46]. Its only assumption is the smoothness of the underlying density. . The second bandwidth s...

Citation Context

...y a linear mapping property [65,p.166]. Our first image segmentation algorithm was a straightforward application of the feature space analysis technique to an L*u*v* representation of the color image =-=[11]-=-. The modularity of the segmentation algorithm enabled its integration by other groups to a large variety of applications like image retrieval [1],face tracking [6],object-based video coding for MPEG-...

Citation Context

...Psi j=1;2::: and n ^fh;K(j)o j=1;2::: converge, and n ^fh;K(j)oj=1;2::: is also monotonically increasing. The proof is given in the Appendix. The theorem generalizes the result derived differently in =-=[13]-=-, where K was the Epanechnikov kernel, and G the uniform kernel. The theorem remains valid when each data point xi is associated with a nonnegative weight wi. An example of nonconvergence when the ker...

Citation Context

...nally, since in most of the cases the decomposition is task dependent, top-down information provided by the user or by an upper-level module can be used to control the kernel bandwidth. We present in =-=[15]-=- a detailed analysis of the bandwidth selection problem. To solve the difficulties generated by the narrow peaks and the tails of the underlying density, two locally adaptive solutions are proposed. O...

Citation Context

...ther hand, adaptively reduce the amount of smoothing near abrupt changes in the local structure,i.e.,edges. There are a large variety of approaches to achieve this goal,from adaptive Wiener filtering =-=[31]-=-,to implementing isotropic [50] and anisotropic [44] local diffusion processes, a topic which recently received renewed interest [19],[37], [56]. The diffusion-based techniques,however,do not have a s...

Citation Context

...ature,we will mention only some whose basic processing relies on the joint domain. In each case,a vector field is defined over the sampling lattice of the image. The attraction force field defined in =-=[57]-=- is computed at each pixel as a vector sum of pairwise affinities between the current pixel and all other pixels,with similarity measured in both spatial and range domains. The region boundaries are t...

Citation Context

... [62, p.108]. For the univariate case a reliable method for bandwidth selection is the plug-in rule [53], which was proven to be superior to least squares cross validation and biased cross-validation =-=[42]-=-, [55, p.46]. Its only assumption is the smoothness of the underlying density. ffl The second bandwidth selection technique is related to the stability of the decomposition. The bandwidth is taken as ...

Citation Context

... representation of the color image [11]. The modularity of the segmentation algorithm enabled its integration by other groups to a large variety of applications like image retrieval [1],face tracking =-=[6]-=-,object-based video coding for MPEG-4 [22],shapedetectionandrecognition[33],andtextureanalysis [47],to mention only a few. However,since the feature space analysis can be applied unchanged to moderate...

Citation Context

...ks retained for the final classification are marked with red dots. 14can be reliably supported by input domain information. The multimodal feature space analysis technique was discussed in detail in =-=[12]-=-. It was shown experimentally that for a synthetic, bimodal normal distribution the technique achieves a classification error similar to the optimal Bayesian classifier. The behavior of this feature s...

Citation Context

...tor computed at that pixel and projected into the spatial domain. However,in contrast to [57],the mean shift procedure moves in the direction of this vector,away from the boundaries. The edge flow in =-=[34]-=- is obtained at each location for a given set of directions as the magnitude of the gradient of a smoothed image. The boundaries are detected at image locations which encounter two opposite directions...

Citation Context

...rs arising from the dominant colors, and a decomposition of the space into elliptical tiles will introduce severe artifacts. Enforcing a Gaussian mixture model over such data is doomed to fail, e.g., =-=[49]-=-, and even the use of a robust approach with contaminated Gaussian densities [67] cannot be satisfactory for such complex cases. Note also that the mixture models require the number of clusters as a p...

Citation Context

...with the requirements to be satisfied by the objective function . The relation between location M-estimators and kernel density estimation is not well investigated in the statistical literature, only =-=[9]-=- discusses it in the context of an edge preserving smoothing technique. 3 Robust Analysis of Feature Spaces Multimodality and arbitrarily shaped clusters are the defining properties of a real feature ...

Citation Context

...than practical importance. 2.6 Relation to Location M-estimators The M-estimators are a family of robust techniques which can handle data in the presence of severe contaminations, i.e., outliers. See =-=[26]-=-, [32] for introductory surveys. In our context only the problem of location estimation has to be considered. 11Given the data and the scale , will define , the location estimator as (30) where, is a...

Citation Context

...ch are based on in situ optimization. Under this paradigm the solution is obtained by using the input domain to define the optimization problem. The in situ optimization is a very powerful method. In =-=[23]-=- and [58] each input data point was associated with a local field (voting kernel) to produce a more dense structure from where the sought information (salient features, the hyperplane representing the...

Citation Context

...never the feature space has more than (say) six dimensions,the analysis should be approached carefully. Employing projection pursuit,in which the density is analyzed along lower dimensional cuts,e.g.,=-=[27]-=-,is a possibility. To conclude,the mean shift procedure is a valuable computational module whose versatility can make it an important component of any computer vision toolbox. APPENDIX Proof of Theore...

Citation Context

...67] cannot be satisfactory for such complex cases. Note also that the mixture models require the number of clusters as a parameter,which raises its own challenges. For example,the method described in =-=[45]-=- proposes several different ways to determine this number. Arbitrarily structured feature spaces can be analyzed only by nonparametric methods since these methods do not have embedded assumptions. Num...

Citation Context

...ractical importance. 2.6 Relation to Location M-estimators The M-estimators are a family of robust techniques which can handle data in the presence of severe contaminations, i.e., outliers. See [26], =-=[32]-=- for introductory surveys. In our context only the problem of location estimation has to be considered. 11Given the data and the scale , will define , the location estimator as (30) where, is a symme...

Citation Context

...lat surface. The connection between anisotropic diffusion and M-estimators is analyzed in [5]. A recently proposed noniterative discontinuity preserving smoothing technique is the bilateral filtering =-=[59]-=-. The relation between bilateral filtering and diffusion-based techniques was analyzed in [3]. The bilateral filters also work in the joint spatial-range domain. The data is independently weighted in ...

Citation Context

...n algorithm enabled its integration by other groups to a large variety of applications like image retrieval [1],face tracking [6],object-based video coding for MPEG-4 [22],shapedetectionandrecognition=-=[33]-=-,andtextureanalysis [47],to mention only a few. However,since the feature space analysis can be applied unchanged to moderately higher dimensional spaces (see Section 5),we subsequently also incorpora...

Citation Context

...4. Optional: Eliminate spatial regions containing less than M pixels. The cluster delineation step can be refined according to a priori information and,thus,physics-based segmentation algorithms,e.g.,=-=[2]-=-,[35],can be incorporated. Since this process is performed on region adjacency graphs,hierarchical techniques like [36] can provide significant speed-up. The effect of the cluster delineation step is ...

Citation Context

... the space. The problem of color representation will be discussed in Section 4,but the employed parameterization has to be carefully examined even in a simple case like the Hough space of lines,e.g., =-=[48]-=-,[61]. The presence of a Mahalanobis metric can be accommodated by an adequate choice of the bandwidth matrix (2). In practice,however,it is preferable to have assured that the metric of the feature s...

Citation Context

... A recently proposed noniterative discontinuity preserving smoothing technique is the bilateral filtering [59]. The relation between bilateral filtering and diffusion-based techniques was analyzed in =-=[3]-=-. The bilateral filters also work in the joint spatial-range domain. The data is independently weighted in the two domains and the center pixel is computed as the weighted average of the window. The f...

Citation Context

...to be known in the statistical literature. While the book [54, Sec.6.2.2] discusses [21], the advantages of employing a mean shift type procedure in density estimation were only recently rediscovered =-=[8]-=-. As will be proven in the sequel a computational module based on the mean shift procedure is an extremely versatile tool for feature space analysis and can provide reliable solutions for many vision ...

Citation Context

... of approaches to achieve this goal,from adaptive Wiener filtering [31],to implementing isotropic [50] and anisotropic [44] local diffusion processes, a topic which recently received renewed interest =-=[19]-=-,[37], [56]. The diffusion-based techniques,however,do not have a straightforward stopping criterion and,after a sufficiently large number of iterations,the processed image collapses into a flat surfa...

Citation Context

...ma of the p.d.f., that is,to the modes of the unknown density. Once the location of a mode is determined,the cluster associated with it is delineated based on the local structure of the feature space =-=[25]-=-,[60],[63]. Our approach to mode detection and clustering is based on the mean shift procedure,proposed in 1975 by Fukunaga and Hostetler [21] and largely forgotten until Cheng's paper [7] rekindled i...

Citation Context

...izes an objective function that expresses the quality of the decomposition (i.e., the index of cluster validity). The objective function typically compares the inter- versus intra-cluster variability =-=[30, 28]-=- or evaluates the isolation and connectivity of the delineated clusters [43]. 15Finally, since in most of the cases the decomposition is task dependent, top-down information provided by the user or b...

Citation Context

...ptional: Eliminate spatial regions containing less than M pixels. The cluster delineation step can be refined according to a priori information and,thus,physics-based segmentation algorithms,e.g.,[2],=-=[35]-=-,can be incorporated. Since this process is performed on region adjacency graphs,hierarchical techniques like [36] can provide significant speed-up. The effect of the cluster delineation step is shown...

Citation Context

...pproaches to achieve this goal,from adaptive Wiener filtering [31],to implementing isotropic [50] and anisotropic [44] local diffusion processes, a topic which recently received renewed interest [19],=-=[37]-=-, [56]. The diffusion-based techniques,however,do not have a straightforward stopping criterion and,after a sufficiently large number of iterations,the processed image collapses into a flat surface. T...

Citation Context

...The modularity of the segmentation algorithm enabled its integration by other groups to a large variety of applications like image retrieval [1],face tracking [6],object-based video coding for MPEG-4 =-=[22]-=-,shapedetectionandrecognition[33],andtextureanalysis [47],to mention only a few. However,since the feature space analysis can be applied unchanged to moderately higher dimensional spaces (see Section ...

Citation Context

...,the index of cluster validity). The objective function typically compares the inter- versus intra-cluster variability [30],[28] or evaluates the isolation and connectivity of the delineated clusters =-=[43]-=-. . Finally,since in most of the cases the decomposition is task dependent,top-down information provided by the user or by an upper-level module can be used to control the kernel bandwidth. We present...

Citation Context

...space. The problem of color representation will be discussed in Section 4,but the employed parameterization has to be carefully examined even in a simple case like the Hough space of lines,e.g., [48],=-=[61]-=-. The presence of a Mahalanobis metric can be accommodated by an adequate choice of the bandwidth matrix (2). In practice,however,it is preferable to have assured that the metric of the feature space ...

Citation Context

...4c. The segmentation step does not add a significant overhead to the filtering process. The region representation used by the mean shift segmentation is similar to the blob representation employed in =-=[64]-=-. However,while the blob has a parametric description (multivariate Gaussians in both spatial and color domain),the partition generated by the mean shift is characterized by a nonparametric model. An ...

Citation Context

...es y j jˆ1;2... and f ^ fh;K…j†g jˆ1;2... converge and f ^ fh;K…j†g jˆ1;2... is monotonically increasing. The proof is given in the Appendix. The theorem generalizes the result derived differently in =-=[13]-=-,where K was the Epanechnikov kernel and G the uniform kernel. The theorem remains valid when each data point xi is associated with a nonnegative weight wi. An example of nonconvergence when the kerne...

Citation Context

..., Sec.3.5] for a readily accessible source for the conversion formulae. The metric of perceptually uniform color spaces is discussed in the context of feature representation for image segmentation in =-=[16]-=-. In practice there is no clear advantage between using or , in the proposed algorithms we employed motivated by a linear mapping property [65, p.166]. Our first image segmentation algorithm was a str...

Citation Context

... stopping criterion and,after a sufficiently large number of iterations,the processed image collapses into a flat surface. The connection between anisotropic diffusion and M-estimators is analyzed in =-=[5]-=-. A recently proposed noniterative discontinuity preserving smoothing technique is the bilateral filtering [59]. The relation between bilateral filtering and diffusion-based techniques was analyzed in...

Citation Context

...Finally,since in most of the cases the decomposition is task dependent,top-down information provided by the user or by an upper-level module can be used to control the kernel bandwidth. We present in =-=[15]-=-,a detailed analysis of the bandwidth selection problem. To solve the difficulties generated by the narrow peaks and the tails of the underlying density,two locally adaptive solutions are proposed. On...

Citation Context

... near abrupt changes in the local structure,i.e.,edges. There are a large variety of approaches to achieve this goal,from adaptive Wiener filtering [31],to implementing isotropic [50] and anisotropic =-=[44]-=- local diffusion processes, a topic which recently received renewed interest [19],[37], [56]. The diffusion-based techniques,however,do not have a straightforward stopping criterion and,after a suffic...

Citation Context

...e amount of smoothing near abrupt changes in the local structure,i.e.,edges. There are a large variety of approaches to achieve this goal,from adaptive Wiener filtering [31],to implementing isotropic =-=[50]-=- and anisotropic [44] local diffusion processes, a topic which recently received renewed interest [19],[37], [56]. The diffusion-based techniques,however,do not have a straightforward stopping criteri...

Citation Context

... u\Lambda v\Lambdasrepresentation of the color image [11]. The modularity of the segmentation algorithm enabled its integration by other groups to a large variety of applications like image retrieval =-=[1]-=-, face tracking [6], object based video coding for MPEG-4 [22], shape detection and recognition [33], and texture analysis [47], to mention only a few. However, since the feature space analysis can be...

Citation Context

...m a severe clustering error,allocation of a few uncertain data points can be reliably supported by input domain information. The multimodal feature space analysis technique was discussed in detail in =-=[12]-=-. It was shown experimentally, that for a synthetic,bimodal normal distribution,the technique achieves a classification error similar to the optimal Bayesian classifier. The behavior of this feature s...

Citation Context

...arametric toolbox developed in this paper is suitable for a large variety of computer vision tasks where parametric models are less adequate,for example,modeling the background in visual surveillance =-=[18]-=-. The complete solution toward autonomous image segmentation is to combine a bandwidth selection technique (like the ones discussed in Section 3.1) with top-down taskrelated high-level information. In...

Citation Context

... practical importance. 2.6 Relation to Location M-Estimators The M-estimators are a family of robust techniques which can handle data in the presence of severe contaminations,i.e., outliers. See [26],=-=[32]-=- for introductory surveys. In our context only,the problem of location estimation has to be considered. Given the data xi; iˆ 1; ...;n; and the scale h,will define ^ ,the location estimator as ^ ˆ arg...

Citation Context

...p.d.f., that is,to the modes of the unknown density. Once the location of a mode is determined,the cluster associated with it is delineated based on the local structure of the feature space [25],[60],=-=[63]-=-. Our approach to mode detection and clustering is based on the mean shift procedure,proposed in 1975 by Fukunaga and Hostetler [21] and largely forgotten until Cheng's paper [7] rekindled interest in...

Citation Context

...nique to an L*u*v* representation of the color image [11]. The modularity of the segmentation algorithm enabled its integration by other groups to a large variety of applications like image retrieval =-=[1]-=-,face tracking [6],object-based video coding for MPEG-4 [22],shapedetectionandrecognition[33],andtextureanalysis [47],to mention only a few. However,since the feature space analysis can be applied unc...

Citation Context

...ture space [25],[60],[63]. Our approach to mode detection and clustering is based on the mean shift procedure,proposed in 1975 by Fukunaga and Hostetler [21] and largely forgotten until Cheng's paper =-=[7]-=- rekindled interest in it. In spite of its excellent qualities,the mean shift procedure does not seem to be known in statistical literature. While the book [54,Section 6.2.2] discusses [21],the advant...

Citation Context

...th the requirements to be satisfied by the objective function …u†. The relation between location M-estimators and kernel density estimation is not well-investigated in the statistical literature,only =-=[9]-=- discusses it in the context of an edge preserving smoothing technique. 3 ROBUST ANALYSIS OF FEATURE SPACES Multimodality and arbitrarily shaped clusters are the defining properties of a real feature ...

Citation Context

...ction 3.5] for a readily accessible source for the conversion formulae. The metric of perceptually uniform color spaces is discussed in the context of feature representation for image segmentation in =-=[16]-=-. In practice,there is no clear advantage between using L*u*v* or L*a*b*; in the proposed algorithms,we employed L*u*v* motivated by a linear mapping property [65,p.166]. Our first image segmentation ...

Citation Context

...ch are based on in situ optimization. Under this paradigm,the solution is obtained by using the input domain to define the optimization problem. The in situ optimization is a very powerful method. In =-=[23]-=- and [58],each input data point was associated with a local field (voting kernel) to produce a more dense structure from where the sought information (salient features,the hyperplane representing the ...

Citation Context

... Considering the univariate case suffices for this purpose. Kernel regression is a nonparametric method to estimate complex trends from noisy data. See [62,chapter 5] for an introduction to the topic,=-=[24]-=- for a more in-depth treatment. Let n measured data points be …Xi;Zi† and assume that the values Xi are the outcomes of a random variable x with probability density function f…x†, xi ˆ Xi; iˆ 1; ...;n...

Citation Context

...rding to a priori information and,thus,physics-based segmentation algorithms,e.g.,[2],[35],can be incorporated. Since this process is performed on region adjacency graphs,hierarchical techniques like =-=[36]-=- can provide significant speed-up. The effect of the cluster delineation step is shown in Fig. 4d. Note the fusion into larger homogeneous regions of the result of filtering shown in Fig. 4c. The segm...

Citation Context

.... 373] used to find the data points falling in the neighborhood of a given kernel. For the efficient Euclidean distance computation,we used the improved absolute error inequality criterion,derived in =-=[39]-=-. 4 APPLICATIONS The feature space analysis technique introduced in the previous section is application independent and,thus,can be used to develop vision algorithms for a wide variety of tasks. Two s...

Citation Context

...od [62,p. 108]. For the univariate case,a reliable method for bandwidth selection is the plug-in rule [53],which was proven to be superior to leastsquares cross-validation and biased cross-validation =-=[42]-=-,[55,p. 46]. Its only assumption is the smoothness of the underlying density. . The second bandwidth selection technique is related to the stability of the decomposition. The bandwidth is taken as the...

Citation Context

...integration by other groups to a large variety of applications like image retrieval [1],face tracking [6],object-based video coding for MPEG-4 [22],shapedetectionandrecognition[33],andtextureanalysis =-=[47]-=-,to mention only a few. However,since the feature space analysis can be applied unchanged to moderately higher dimensional spaces (see Section 5),we subsequently also incorporated the spatial coordina...

Citation Context

...sters arising from the dominant colors and a decomposition of the space into elliptical tiles will introduce severe artifacts. Enforcing a Gaussian mixture model over such data is doomed to fail,e.g.,=-=[49]-=-, and even the use of a robust approach with contaminated Gaussian densities [67] cannot be satisfactory for such complex cases. Note also that the mixture models require the number of clusters as a p...

Citation Context

...sed on in situ optimization. Under this paradigm,the solution is obtained by using the input domain to define the optimization problem. The in situ optimization is a very powerful method. In [23] and =-=[58]-=-,each input data point was associated with a local field (voting kernel) to produce a more dense structure from where the sought information (salient features,the hyperplane representing the fundament...

Citation Context

... the p.d.f., that is,to the modes of the unknown density. Once the location of a mode is determined,the cluster associated with it is delineated based on the local structure of the feature space [25],=-=[60]-=-,[63]. Our approach to mode detection and clustering is based on the mean shift procedure,proposed in 1975 by Fukunaga and Hostetler [21] and largely forgotten until Cheng's paper [7] rekindled intere...

Citation Context

...ptical tiles will introduce severe artifacts. Enforcing a Gaussian mixture model over such data is doomed to fail,e.g.,[49], and even the use of a robust approach with contaminated Gaussian densities =-=[67]-=- cannot be satisfactory for such complex cases. Note also that the mixture models require the number of clusters as a parameter,which raises its own challenges. For example,the method described in [45...

Citation Context

... of the p.d.f., that is, to the modes of the unknown density. Once the location of a mode is determined, the cluster associated with it is delineated based on the local structure of the feature space =-=[25, 60, 63]-=-. Our approach to mode detection and clustering is based on the mean shift procedure, proposed in 1975 by Fukunaga and Hostetler [21] and largely forgotten till Cheng's paper [7] rekindled the interes...

Citation Context

...4. Optional: Eliminate spatial regions containing less than M pixels. The cluster delineation step can be refined according to a priori information and,thus,physics-based segmentation algorithms,e.g.,=-=[2]-=-,[35],can be incorporated. Since this process is performed on region adjacency graphs,hierarchical techniques like [36] can provide significant speed-up. The effect of the cluster delineation step is ...

Citation Context

.... Considering the univariate case suffices for this purpose. Kernel regression is a nonparametric method to estimate complex trends from noisy data. See [62, Chap.5] for an introduction to the topic, =-=[24]-=- for a more in-depth treatment. Let measured 10data points be and assume that the values are the outcomes of a random variable with probability density function , , while the relation between and is ...