5th Intensive Course on Soil Micromorphology Naples th - 14th September Image Analysis Lecture 8 Introduction to Binary Morphology

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Erosion/Dilation Opening/Closing Kernel Shapes Applications in Particle / Void Size Distribution Introduction to Binary Morphology Methods Requires Segmentation of Image into Binary Form (may require manual editting). Foreground pixels are coded 1 - background 0 i.e. Particles 1 (white), voids 0 (black) or Voids 1 (white), particles 0 (black)

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Erosion strips one layer of foreground pixels at edges of particles criteria based on number of surrounding background pixels can be any number pixel of interest is red white - foreground black - background

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology a) foreground pixel removed for all criteria. h) foreground pixel removed only if criteria is set to 1 pixel. Criteria may also specify that diagonal erosion is (or is not permitted). Erosion not permitted if diagonals not allowed in (j)

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Connectivity: 4 - point connectivity allows connection only up/down and side to side 8 - point connectivity allows connection on diagonals In 4 - point connectivity, foreground and background are uniquely separated. In 8 - point connectivity is background or foreground continuous across diagonal? Both are not possible

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Erosion of original by one layer criterion - a single touching background pixel 4 - point connectivity8 - point connectivity

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Erosion by 2 and 3 layers 4 - point connectivity Some residual parts of largest particle remain. Erosion by 2 and 3 layers 8 - point connectivity All foreground features will disappear. Until particles disappear the residues are less rough

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Dilation - the reverse of erosion Once again similar criteria apply 8 - point connectivity 4 - point connectivity Individual features will merge

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology 8 - point connectivity erosion Equivalent to passing a 3 x 3 kernel over binary image. Where central point of kernel hits background, all pixels covered by kernel are set to background

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology 4 - point connectivity erosion Equivalent to passing a 3 x 3 kernel over binary image. Where central point of kernel hits background, all pixels covered by kernel are set to background

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Non-standard Kernels may be used for special effects

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Consider effect of one erosion followed by one dilation. This is known as an OPENING

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Red: Residual after erosion Yellow: Recovered after dilation Blue: Complete particles lost Green: Roughness lost on large particles Using careful housekeeping it is possible to identify proportion of particles lost completely and roughness lost from large particles.

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology 2 cycles of erosion (8 - point connectivity) 2 cycles of erosion followed by 2 cycles of dilation (8 - point connectivity) Components of opening - see next slide

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Light Green: Roughness cycle 1 Dark Green: Roughness cycle 2 Red: Residue after 2 cycles Yellow: Recovery cycle 1 Orange: Recovery cycle 2 Blue: Particles lost cycle 1 Purple: Particles lost cycle 2

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology 2 cycles of 3 x 3 kernel are equivalent to 1 cycle by a 5 x 5 kernel. Can be used for efficiency Alternative kernel for 5 x 5 which approximates more closely to a circle (i.e. corner pixels are omitted) Kernel for 3 cycles giving a good approximation to a circle / octagon).

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Standard Kernels for 9 x 9 array These 4 shapes can be propagated to any size

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Procedure for feature size analysis Erode n cycles Dilate n cycles Determine pixels lost as roughness Determine pixels lost from particles which disappear n = 1 Are particle residues left Yes No n = n + 1 Summarise results

Schematic Representation of one erosion and one dilation Grey Level Image Binary Version 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology

BINARY MORPHOLOGY During successive opening, features tend towards circles. At each stage, protrusions are lost and this loss is related to the shape and roughness of grains. Finally, the remaining feature is lost and this is related to the size of the feature. Careful housekeeping is needed to differentiate between two types of loss, but procedure is well established in some branches of microscopy. The difficulty in achieving a reliable threshold makes the method generally unsuitable for analysing images of cores. 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology

Binary Morphology used to determine Particle size Distribution 5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Roundness Often defined relating to sharpness of asperities on a grain Sometimes roundness is defined by drawing circles, but when exactly should on draw a circle?

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Grain is successively opened with different radii. The lighter colours (yellow) show parts lost first. Ultimately remainder of grain disappears when inscribed circle is as shown in blue. If octagonal or square structuring elements are used, then grain degenerates to these shapes.

5th Intensive Course on Soil Micromorphology - Naples 2001 Image Analysis - Lecture 8: Binary Morphology Grain is successively subjected to opening of different radii. The edge of the grain are shown in colour where light colours (e.g. yellow represent areas lost first - i.e. sharp), and dark colours (e.g. dark blue are lost last. Can be used as a more objective measure of roundness.