Image Thresholding

We have numbers for the photograph, but Botie still needs to know which positions might belong to a seed. In this image the seeds are light and the tray is dark. That gives us a simple starting point: mark positions whose intensity exceeds a chosen cutoff.

Before asking a model to learn that rule, let's see what we get by writing it ourselves. We will also move a shadow across the tray, because a rule that works under one lamp may not work under another.

Raise the cutoff through the image's brightness values. Watch selected positions disappear, then compare the number of selected pixels with the number of objects you can see.

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A binary mask keeps the shape of the image but stores a yes-or-no decision at each position. In our convention, one means foreground and zero means background. NumPy comparisons first produce Boolean values; convert to integers when we want to display zeros and ones.

We must specify what happens at the cutoff. Here, a pixel equal to the cutoff remains background.

mask[row, column] = 1 if image[row, column] > cutoff else 0
100 > 100 is False
101 > 100 is True

Foreground means the rule selected that position. It does not establish that the position really belongs to a seed.

If we add the mask's ones, we count selected pixels. Taking its mean gives the selected fraction of the image. But Botie wanted seeds, and one seed can occupy many pixels.

Put the mask beside the photograph. Does the selected region follow each seed? That is the first check to make before we try to turn regions into an object count.

Selected pixels = 2
Total pixels = 9
Selected share = 2 / 9 ≈ 0.2222

Two selected pixels in this tiny image describe one connected region. A later lesson will make that distinction explicit.

import numpy as np
image = np.array([[10,20,10], [20,220,30], [10,200,20]])
mask = image > 100
print(mask.astype(int).tolist())
print(int(mask.sum()))

[[0, 0, 0], [0, 1, 0], [0, 1, 0]]
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Lowering the cutoff admits more pixels. This may recover a dim seed, but it can also include the tray. Raising it does the reverse. Choose a cutoff using representative training or development images, then check it on held-out images.

A histogram counts how many pixels have each intensity. A gap between dark and bright groups suggests possible cutoffs. Otsu's method formalises a particular criterion for selecting one from that histogram.

A histogram ignores where pixels are located. Two images with the same histogram receive the same Otsu threshold even if their objects are arranged differently.

Uneven illumination changes the background across a photograph. A local threshold compares a pixel with a reference estimated around that position, often a local mean or weighted mean with an offset.

The neighbourhood must be chosen carefully. If it is too small, the object itself can dominate the reference. If it is too large, the reference may fail to follow illumination changes. Border padding also affects these local estimates.

Example local reference = 70
Chosen offset = 5
Local cutoff = 70 - 5 = 65
Pixel intensity = 80
80 > 65, so this rule selects the pixel

The offset's sign here follows a mean-minus-offset convention. Local thresholding adds assumptions; it does not guarantee correct segmentation.

The mask is a useful intermediate result. We can clean small speckles, find connected regions, or measure selected area. But a brightness rule cannot recognise an object whose appearance overlaps with the background.

In the workshop, produce the mask and count the selected pixels. Try an equal-to-cutoff value and an entirely dark tray as well as the original example.

We will address shapes and connected regions next. A learned segmentation model becomes useful when the decision requires more than a brightness comparison.

A shadow can make a seed darker than a well-lit patch of tray. No single intensity cutoff then separates both correctly. Moving the cutoff merely trades one kind of mistake for another.

Inspect the photograph and mask together. Local reference rules, controlled lighting or a learned segmenter can address different causes of failure. Do not keep adjusting a global threshold when the required distinction is absent from the intensity alone.

A supervised assessment needs a mask that states which pixels belong to the seed. Count overlap and extra selected pixels against that reference. Intersection over union penalises both missed seed pixels and selected background.

An all-background prediction can have high pixel accuracy when seeds occupy little of the image. That is why the metric must reflect the foreground task. Specify how empty prediction and empty reference masks are handled.

import numpy as np
truth = np.array([[0,1,1],[0,1,0]], dtype=bool)
pred = np.array([[0,1,0],[0,1,1]], dtype=bool)
intersection = (truth & pred).sum()
union = (truth | pred).sum()
print(int(intersection), int(union))
print(float(intersection/union))

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0.5