Geometric feature learning

Key takeaways

Geometric feature learning belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Geometric feature learning to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Geometric feature learning from memory before moving on to harder problems.

Reference excerpt

Geometric feature learning is a technique combining machine learning and computer vision to solve visual tasks. The main goal of this method is to find a set of representative features of geometric form to represent an object by collecting geometric features from images and learning them using efficient machine learning methods. Humans solve visual tasks and can give fast response to the environment by extracting perceptual information from what they see. Researchers simulate humans' ability of recognizing objects to solve computer vision problems. For example, M. Mata et al.(2002) applied feature learning techniques to the mobile robot navigation tasks in order to avoid obstacles. They used genetic algorithms for learning features and recognizing objects (figures). Geometric feature learning methods can not only solve recognition problems but also predict subsequent actions by analyzing a set of sequential input sensory images, usually some extracting features of images. Through learning, some hypothesis of the next action are given and according to the probability of each hypothesis give a most probable action. This technique is widely used in the area of artificial intelligence.

Introduction Geometric feature learning methods extract distinctive geometric features from images. Geometric features are features of objects constructed by a set of geometric elements like points, lines, curves or surfaces. These features can be corner features, edge features, Blobs, Ridges, salient points image texture and so on, which can be detected by feature detection methods.

Geometric features Primitive features Corners: Corners are a very simple but significant feature of objects. Especially, Complex objects usually have different corner features with each other. Corners of an object can be extracted through Corner detection. Cho and Dunn used a different way to define a corner by the distance and angle between two straight line segments. This is a new way by defining features as a parameterized composition of several components. Edges: Edges are one-dimensional structure features of an image. They represent the boundary of different image regions. The outline of an object can be easily detected by finding the edge using the technique of edge detection. Blobs: Blobs represent regions of images, which can be detected using blob detection method. Ridges: From a practical viewpoint, a ridge can be thought of as a one-dimensional curve that represents an axis of symmetry. Ridges detection method-see ridge detection salient points-see Kadir–Brady saliency detector image texture Compound features Geometric composition Geometric component feature is a combination of several primitive features and it always consists more than 2 primitive features like edges, corners or blobs. Extracting geometric feature vector at location x can be computed according to the reference point, which is shown below:

x i = x i − 1 + σ i − 1 d i [ cos ⁡ ( θ i − 1 + ϕ i ) sin ⁡ ( θ i − 1 + ϕ i ) ] {\displaystyle \textstyle \ x_{i}=x_{i-1}+\sigma _{i-1}d_{i}{\begin{bmatrix}\cos(\theta _{i-1}+\phi _{i})\\\sin(\theta _{i-1}+\phi _{i})\end{bmatrix}}}

θ i = θ i − 1 + Δ θ i {\displaystyle \textstyle \ \theta _{i}=\theta _{i-1}+\Delta \theta _{i}}

σ i = σ i − 1 Δ σ i {\displaystyle \textstyle \ \sigma _{i}=\sigma _{i-1}\Delta \sigma _{i}}

x means the location of the location of features, θ {\displaystyle \textstyle \theta } means the orientation, σ {\displaystyle \textstyle \sigma } means the intrinsic scale.

Boolean Composition Boolean compound feature consists of two sub-features which can be primitive features or compound features. There are two type of boolean features: conjunctive feature whose value is the product of two sub-features and disjunctive features whose value is the maximum of the two sub-features.

Feature space Feature space was firstly considered in computer vision area by Segen. He used multilevel graph to represent the geometric relations of local features.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Geometric feature learning

Start with the simplest possible case. Write down what Geometric feature learning claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Geometric feature learning before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Geometric feature learning ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Geometric feature learning

In research: Geometric feature learning appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Geometric feature learning in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Geometric feature learning is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applications of computer vision, Feature detection (computer vision), Machine learning, so understanding it makes those chapters shorter.
In everyday life: Look for Geometric feature learning outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Geometric feature learning in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Geometric feature learning means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Geometric feature learning out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Geometric feature learning in simple terms?

Geometric feature learning is a technique combining machine learning and computer vision to solve visual tasks. The main goal of this method is to find a set of representative features of geometric form to represent an object by collecting geometric features from images and learning them using effi…

Why does Geometric feature learning matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Geometric feature learning?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Geometric feature learning.