Computer vision asks a machine to do something a person does without
thinking: look at a picture and say what's in it, where it is, or how far
away it sits. Every technique this course builds toward — detecting a
face, stitching two photos into a panorama, reconstructing a 3D scene from
two camera views, letting a robot recognize a doorway — starts from the
same object digital-image-processing already spent a full course on: a
grid of numbers. This chapter is not a re-teaching of that course. It is a
fast, working-depth pass through the six specific tools this course reaches
for constantly — tensors and coordinates, convolution, gradients, the
frequency domain, segmentation, and eigen-decomposition — each restated
here in this course's own voice and pointed at what's coming, plus one
genuinely new idea this course needs before Chapter 11: what a neuron
computes and how a network's weights get adjusted during training, at the
shallow, working depth this course needs and no deeper.
If a fact here feels familiar from digital-image-processing or
linear-algebra, that's intentional — this chapter still states it, still
derives the piece worth deriving, and still works a fresh example, in this
course's own notation, rather than sending you elsewhere to find it. The
one exception is Section 7: deep-learning owns the full mathematics of
neurons and how a network is trained, and this course doesn't require it
as a prerequisite, so that section teaches only enough to follow this
course's own Chapter 11 — a primer, not a substitute for that course.
Section 1 fixes how this course's own vision-model chapters will describe
an image's shape once a "batch" of many images enters the picture — the one
idea in this chapter that's genuinely new. Sections 2–6 recall convolution
and kernels, image gradients and edges, the frequency domain, thresholding
and clustering-based segmentation, and PCA/eigen-decomposition — six tools
Chapters 2 through 20 all lean on directly. Section 7 closes with the
neuron/training primer. Deeper background and full proofs stay one
:::review pull away in whichever course first built each fact; nothing in
this chapter depends on you opening it.