Channel smoothing: efficient robust smoothing of low-level signal features

Abstract

In this paper we present a new and efficient method to implement robust smoothing of low-level signal features: B-spline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that linear smoothing of channels is equivalent to robust smoothing of the signal features if we make use of quadratic B-splines to generate the channels. The linear decoding from B-spline channels allows the derivation of a robust error norm, which is very similar to Tukey's biweight error norm. We compare channel smoothing with three other robust smoothing techniques: non-linear diffusion, bilateral filtering, and mean-shift filtering, both theoretically, and on a 2D orientation-data smoothing task. Channel smoothing is found to be superior in four respects: it has a lower computational complexity, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on non-linear spaces, such as orientation space.

Weighted Update and Comparison for Channel-Based Distribution Field Tracking

“…Readers unfamiliar with these methods are referred to more comprehensive descriptions in literature [6,2,3] for details.…”

“…This computational efficiency allows for computing channel representations at each image pixel or for small image neighborhoods, as used in channel smoothing [2] as a variant of bilateral filtering [8], and tracking using distribution fields [4].…”

“…In most cases v 1 such that K is of moderate size. The smooth kernel of the channel representation reduces the quantization effect compared to histograms by a factor of up to 20 in practice [2]. This allows reduction of the computational load by using fewer bins or to increase the accuracy for the same number of bins.…”

Incremental Computation of Feature Hierarchies

“…Channel representations as a computational framework, e.g. for object recognition, have been introduced in [10], and are directly related to kernel density estimation [11]. Channel representations of features are basically soft-histograms or Parzen estimators with a smooth kernel function.…”

“…Channel representations of features are basically soft-histograms or Parzen estimators with a smooth kernel function. They are beneficial in many tasks due to their robustness [11,23].…”