Element-Weighted Neutrosophic Correlation Coefficient and Its Application in Improving CAMShift Tracker in RGBD Video

Abstract

Neutrosophic set (NS) is a new branch of philosophy to deal with the origin, nature, and scope of neutralities. Many kinds of correlation coefficients and similarity measures have been proposed in neutrosophic domain. In this work, by considering that there may exist different contributions for the neutrosophic elements of T (Truth), I (Indeterminacy), and F (Falsity), a method of element-weighted neutrosophic correlation coefficient is proposed, and it is applied for improving the CAMShift tracker in RGBD (RGB-Depth) video. The concept of object seeds is proposed, and it is employed for extracting object region and calculating the depth back-projection. Each candidate seed is represented in the single-valued neutrosophic set (SVNS) domain via three membership functions, T, I, and F. Then the element-weighted neutrosophic correlation coefficient is applied for selecting robust object seeds by fusing three kinds of criteria. Moreover, the proposed correlation coefficient is applied for estimating a robust back-projection by fusing the information in both color and depth domains. Finally, for the scale adaption problem, two alternatives in the neutrosophic domain are proposed, and the corresponding correlation coefficient between the proposed alternative and the ideal one is employed for the identification of the scale. When considering challenging factors like fast motion, blur, illumination variation, deformation, and camera jitter, the experimental results revealed that the improved CAMShift tracker performs well.Information 2018, 9, 126 2 of 16 in a solution deemed to be satisfactory. It has been applied for residential house garage location selection [18], element and material selection [19], and sustainable market valuation of buildings [20]. For the application of image segmentation, several criteria in the NS domain were usually proposed for calculating a specific neutrosophic image [5][6][7][8][9]. The correlation coefficient between SVNSs [17] was applied for calculating a neutrosophic score-based image [9], and a robust threshold was estimated by employing the OTSU's method [9]. In [11], two criteria were proposed in both color and depth domain. The information fusion problem was converted into a multicriteria decision-making issue, and the single-valued neutrosophic cross-entropy was employed to tackle this problem [11]. For the neutrosophic theory-based MeanShift tracker [12], by taking the consideration of the background information and appearance changes between frames, two kinds of criteria were considered, the object feature similarity and the background feature similarity. The SVNS correlation coefficient [17] was applied for calculating the weighted histogram, and then the histogram was finally used to enhance the traditional MeanShift tracker. Besides the fields mentioned above, the NS theory was also introduced into clustering algorithms such as c-means [21]. While NS-based correlation coefficients have been widely used for solving some engineering issues, the weights of the three membership fu...

Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model

“…Step 3. By use of Equation (12) for SVNSs or Equation (13) for INSs, the improved weighted SM between Y i (i = 1, 2, . .…”

“…for INSs. (13) Since Equations (12) and (13) are the weighted normalized SMs of SVNSs and INSs, they also satisfy these conditions: W k (X, Y) = W k (Y, X) and 0 ≤ W k (X, Y) ≤ 1 for k = 1, 2.…”

“…Since a neutrosophic set (NS) [1] provides an effective way to express inconsistent, incomplete, and indeterminate information in the real world, which cannot be expressed by the fuzzy set and (interval-valued) intuitionistic fuzzy set [2][3][4][5], it has been widely applied in various fields, such as image processing [6][7][8][9], object tracking [10][11][12], and decision-making [13]. As a subclass of NS, a simplified neutrosophic set (SNS) [14], implying single-valued neutrosophic set (SVNS) and interval neutrosophic set (INS) concepts, is composed of the truth, indeterminacy, and falsity components, where their membership degrees are constrained in the real standard interval [0,1].…”

Online Visual Tracking of Weighted Multiple Instance Learning via Neutrosophic Similarity-Based Objectness Estimation

“…To adjust these challenges adaptively, it is quite important for a robust object tracker to employ an effective appearance model. In general, the existing appearance models can be mainly divided into two categories, the generative model [3][4][5][6][7][8][9] and the discriminative model [10][11][12][13][14][15][16][17][18]. For the generative model, the tracking is cast as finding the most similar region to the learned object appearance.…”

“…It has been widely used in dealing with uncertain information [23]. Due to this, the NS theory has been successfully introduced into many applications, such as medical diagnosis [24], skeleton extraction [25], image segmentation [26][27][28][29][30][31], and object tracking [7][8][9]32]. SVNS (single valued neutrosophic set) [33] is a subclass of the neutrosophic set with a finite interval for practical usage.…”