Morphology, Binary Images & Shape

Chapter Overview

Walk into almost any modern factory and find the machine-vision cabinet. Inside it, a camera stares at a backlit conveyor, and a program decides, hundreds of times per minute, whether each passing part ships or gets rejected. The deciding code is rarely a neural network. More often it is a threshold, a couple of erosions and dilations, a connected-component pass, and three or four measured numbers compared against a spec sheet. This pipeline runs in microseconds, fails in ways an engineer can explain to a regulator, and has quietly inspected most of the bottles, pills, circuit boards, and engine parts manufactured since the 1980s. This chapter is about that pipeline: what happens after an image becomes binary.

Binary images are where the previous chapters have been heading. Chapter 2 built the thresholding machinery that converts grayscale into foreground and background, and the document scanner of Chapter 5 ends by binarizing a rectified page. But raw thresholds are messy: salt speckle where sensor noise crossed the line, pinholes where glare punched through an object, ragged edges, accidental bridges between touching parts. Section 6.1 lays the foundations needed to even talk about this mess precisely: what a binary image is as a set, how pixels become neighbors, and why the innocent-looking question "are these two pixels connected?" has a paradox at its center. Section 6.2 then introduces the two atoms of mathematical morphology, erosion and dilation: a small probe shape called a structuring element slides over the image and votes each pixel off or onto the island.

Atoms become molecules in Section 6.3. Composing erosion and dilation in opposite orders yields opening and closing, the workhorse cleanup operators that remove speckle and fill pinholes while leaving everything larger untouched; their differences yield morphological gradients and the top-hat transforms that rescue thresholding from uneven illumination. With a clean mask in hand, Section 6.4 crosses the most important bridge in classical vision: from pixels to objects. Connected-component labeling gives every blob an identity, and region properties (area, centroid, eccentricity, solidity, hole count) turn each identity into a row of measurements ready for a decision rule.

The last two sections deepen what "shape" means. Section 6.5 introduces the distance transform, which answers "how far is every pixel from the boundary?" in one pass and, with it, finds the widest point of a part, separates touching objects, and collapses elongated structures onto their skeletons for length and width measurement. Section 6.6 traces object boundaries into contours, compresses them into moments and invariant descriptors, and assembles a complete shape classifier in a page of code: a small preview of the classical recognition pipelines of Chapter 16.

This chapter also continues one of the book's arcs and starts another. The thresholding-to-binary thread that began in Chapter 2 runs through every page here and resurfaces in Chapter 24, where neural networks output per-pixel probabilities that are thresholded into exactly the masks this chapter manipulates; the cleanup and measurement tools you learn here are the standard post-processing behind modern segmentation models. And the distance transforms and skeletons of Section 6.5 return as watershed seeds in Chapter 11, as boundary-aware losses in segmentation training, and as signed distance fields in the 3D representations of Chapter 27.