Morphological Image Processing Extracting meaning by dilation erosion

Morphological Image Processing Extracting meaning by dilation, erosion, opening, and closing… DRAFT: Copyright GA Tagliarini, Ph. D

Half-tone Examples l l 2 Laser printed images Old newspaper images 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Notation From Set Theory 3 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Examples A B A A A B B A B 4 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

The Cross-product 5 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Focus On Half-toned Images l l l 6 Morphological image processing assumes objects that are represented in images using only two “color” values say black and white. The coordinates of the black (or white) pixels form a complete description of the objects in the image. An object in a half-toned image is specified completely as a subset A of Z 2 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Notation Specific To Morphological Processing 7 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Dilation By A Circular Structuring Element B A 8 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Dilation: By A Rectangular Structuring Element B A 9 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Dilation: By A Structuring Element Whose Reflection Is Not Itself A 10 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Erosion: By A Circular Structuring Element B A 11 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Erosion: By A Rectangular Structuring Element B A 12 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Erosion: By A Structuring Element Whose Reflection Is Not Itself A 13 AO B 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Dilation and Erosion l Dilation – – l Expands or inflates an object Fills in gaps Erosion – – Contracts an object Depending upon the structuring element l l 14 May exaggerate openings May eliminate all but a skeleton of the object 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening and Closing 15 l Opening is erosion followed by dilation l Closing is dilation followed by erosion 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening: By A Circular Structuring Element B A 16 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening: By A Circular Structuring Element B B A 17 A 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening: By A Rectangular Structuring Element B A 18 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening: By A Rectangular Structuring Element B A 19 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening: By A Structuring Element Whose Reflection Is Not Itself A 20 AO B 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Opening: By A Structuring Element Whose Reflection Is Not Itself A 21 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D

Closing By A Circular Structuring Element B A 22 1/11/2022 DRAFT: Copyright GA Tagliarini, Ph. D