A robust kernel density estimator based mean-shift algorithm

Abstract

We propose a robustification of the mean-shift algorithm. We understand robustness in the statistical sense as the deviation from the nominal, distributional assumption. The derivation of the robust mean-shift vector is based on a robust version of the kernel density estimator (KDE), where the KDE is interpreted as an inner product in a higher dimensional feature space. The mean in this formulation is replaced by an Mestimate in order to robustify against outlying data points. We show the superiority of our algorithm compared to the standard mean-shift algorithm and to the median-shift algorithm using both simulated and real data in both contaminated and uncontaminated data. The real data stems from an image segmentation application for blood glucose measurement.

Measuring Blood Glucose Concentrations in Photometric Glucometers Requiring Very Small Sample Volumes

“…where the robust weights w R-MS l can be determined using Iteratively ReWeighted Least Squares (IRWLS) [9], [28], resulting in…”

“…It has been widely applied for medical image segmentation as it does not require the knowledge of the actual number of clusters [8], [19]- [22]. We use the mean-shift algorithm (MS), as well as two extensions of it: the robust mean-shift (R-MS) [9] and the scalable, sparse mean-shift (SS-MS) [10]. Furthermore, we extend these variants to the medoid-shift [23].…”

“…2) The Robust Mean-Shift Algorithm: In [9], the robust mean-shift (R-MS) is derived as an alternative to account for heavy-tailed noise in the data. Here, the sample mean of vectors in Eq.…”

“…, n C without prior knowledge on the number or shape of the regions. We build up on our previous work in [8], [9], by incorporating the median instead of the mean which exhibits better performance, as well as, providing convergence proofs for all the derived methods. Furthermore, a data-driven heuristic is introduced to choose the subset size individually for the scalable version, which further reduces the subset size in most cases; (iii) the derivation of a model for the chemical kinetics that is incorporated in a temporal tracking and prediction setup to enhance accuracy and reduce measurement time drastically; (iv) the mapping of the estimated remission to the underlying glucose concentration.…”

“…Using these sets, we are able to identify a minimum range for the blood sample volume to maintain the required accuracy. We note that some aspects of this work appeared in [8], [9] and [10], while the substantial part of this manuscript is novel. Some notation: In this work, scalars are represented by lower case, non-bold letters a, while lower case bold letters denote vectors a and a l indicates the l-th element of the vector.…”