On the Use of Low-Pass Filters for Image Processing with Inverse Laplacian Models

Abstract

A novel signal processing-oriented approach to solving problems involving inverse Laplacians is introduced. The Monogenic Signal is a powerful method of computing the phase of discrete signals in image data, however it is typically used with band-pass filters in the capacity of a feature detector. Substituting low-pass filters allows the Monogenic Signal to produce approximate solutions to the inverse Laplacian, with the added benefit of tunability and the generation of three equivariant properties (namely local energy, local phase and local orientation), which allow the development of powerful numerical solutions for a new set of problems. These principles are applied here in the context of biological cell segmentation from brightfield microscopy image data. The Monogenic Signal approach is used to generate reduced noise solutions to the Transport of Intensity Equation for optical phase recovery, and the resulting local phase and local orientation terms are combined in an iterative level set approach to accurately segment cell bound-

Using the Monogenic Signal for Cell-Background Classification in Bright-Field Microscope Images

“…We have empirically showed that the pixelwise cell-background classification yields considerably better results when the local phase as obtained in [7] is used instead of the defocused image. Nevertheless, the defocused image still delivers better results compared to the at-focus image.…”

“…Like its 1D counterpart, it is computed in practice by convolving the signal with a band-pass quadrature filter yielding the local phase and local energy of the input. In [7], a link between the physical phase and the local phase was established using the monogenic signal. According to [7], it is possible to use the monogenic signal framework to approximate the solution of equation (1) under two conditions: First, the derivative image, i.e.…”

“…In [7], a link between the physical phase and the local phase was established using the monogenic signal. According to [7], it is possible to use the monogenic signal framework to approximate the solution of equation (1) under two conditions: First, the derivative image, i.e. the left side of equation (1), is used as an input instead of the image itself.…”

“…A QPM approach in [7] suggests approximating the TIE (section 2.1) solution in the monogenic signal (section 2.2) domain. In fact, the obtained results approximate the local phase and the local energy of the physical light phase.…”

Automatic segmentation of adherent biological cell boundaries and nuclei from brightfield microscopy images

“…[21]). We recently outlined a possible mathematical connection, based on filter theory, between the two fields in a separate paper [4]. The advantages of our low-pass filter approach, compared with the phase recovery method of Paganin et al, are that it significantly reduces low-frequency noise associated with conventional phase recovery, and it also provides local orientation information which can be used to improve our algorithm.…”