Α-scale Space Kernels in Practice

نویسندگان

  • Frans Kanters
  • Luc Florack
  • Remco Duits
  • Bram Platel
چکیده

Kernels of a so-called α-scale space ( 12 < α < 1) have the undesirable property that there is no closed-form representation in the spatial domain, despite their simple closedform expression in the Fourier domain. This obstructs a spatial convolution or recursive implementation. For this reason an approximation of the 2D α-kernel in the spatial domain is presented using the well known Gaussian kernel (α = 1) and the Poisson kernel (α = 12 ). Experiments show good results, with maximum relative errors of less than 2.4%.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Comparison of the Deep Structure of α-Scale Spaces

We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x, s) ∈ R × R | s > 0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson sc...

متن کامل

Modeling spatio-temporal nonlocality in mean-field dynamos

When scale separation in space and time is poor, the α effect and turbulent diffusivity have to be replaced by integral kernels. Earlier work in computing these kernels using the test-field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel is such that it can be treated in a straightforward manner by solving a...

متن کامل

Scalable Alignment Kernels via Space-Efficient Feature Maps

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVMs in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, ...

متن کامل

Building New Kernel Family with Compact Support, in Scale-Space

Scale-space representation is one formulation of the multi-scale representation which has received considerable interest in the literature, because of its efficiency in several practical applications, and the distinct properties of the Gaussian kernel which generates the Scale-space. However, in practice, we note some undesirable limitations when using the Gaussian kernel: information loss caus...

متن کامل

A Novel Method for Generating Scale Space Kernels Based on Wavelet Theory

The linear scale-space kernel is a Gaussian or Poisson function. These functions were chosen based on several axioms. This representation creates a good base for visualization when there is no information (in advanced) about which scales are more important. These kernels have some deficiencies, as an example, its support region goes from minus to plus infinite. In order to solve these issues se...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004