Locally Adaptable Mathematical Morphology Using Distance Transformations

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels. We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be e±ciently implemented as a variant of distance trans- formation algorithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation

Grey-scale 1-D dilations with spatially-variant structuring elements in linear time

Full text also available online for free at http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/International audienceSpatially variant morphological operators can significantly improve filtering capabilities or object detection score of various applications. Whereas an effort has been made to define the theoretical background, the efficient implementation of adaptable algorithms remained far less considered. In this paper, we present an efficient,one-scan, linear algorithm for 1-D grey-scale dilations/erosions with spatially variant structuring elements. The proposed algorithm processes data in stream, can work in place and produces results with minimal latency. The computing time is independent of the structuring element size

Incremental Distance Transforms (IDT)

A new generic scheme for incremental implementations of distance transforms (DT) is presented: Incremental Distance Transforms (IDT). This scheme is applied on the cityblock, Chamfer, and three recent exact Euclidean DT (E2DT). A benchmark shows that for all five DT, the incremental implementation results in a significant speedup: 3.4×−10×. However, significant differences (i.e., up to 12.5×) among the DT remain present. The FEED transform, one of the recent E2DT, even showed to be faster than both city-block and Chamfer DT. So, through a very efficient incremental processing scheme for DT, a relief is found for E2DT’s computational burden

Adaptivity and group invariance in mathematical morphology

The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depend on image location or on image features. Another one is to extend translation invariance to more general invariance groups, where the shape of the structuring element spatially adapts in such a way that global group invariance is maintained. We review group-invariant morphology, discuss the relations with adaptive morphology, point out some pitfalls, and show that there is no inherent incompatibility between a spatially adaptive structuring element and global translation invariance of the corresponding morphological operators

Spatially-Variant Directional Mathematical Morphology Operators Based on a Diffused Average Squared Gradient Field

International audienceThis paper proposes an approach for mathematical morphology operators whose structuring element can locally adapt its orientation across the pixels of the image. The orientation at each pixel is extracted by means of a diffusion process of the average squared gradient field. The resulting vector field, the average squared gradient vector flow, extends the orientation information from the edges of the objects to the homogeneous areas of the image. The provided orientation field is then used to perform a spatially variant filtering with a linear structuring element. Results of erosion, dilation, opening and closing spatially-variant on binary images prove the validity of this theoretical sound and novel approach

Morphological bilateral filtering

International audienceA current challenging topic in mathematical morphology is the construction of locally adaptive operators; i.e., structuring functions that are dependent on the input image itself at each position. Development of spatially-variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the first part of the paper is to study how to generalize these convolution-based approaches in order to introduce adaptive nonlinear filters that asymptotically correspond to spatially-variant morphological dilation and erosion. In particular, starting from the bilateral filtering framework and using the notion of counter-harmonic mean, our goal is to propose a new low complexity approach to define spatially-variant bilateral structuring functions. Then, in the second part of the paper, an original formulation of spatially-variant flat morphological filters is proposed, where the adaptive structuring elements are obtained by thresholding the bilateral structuring functions. The methodological results of the paper are illustrated with various comparative examples