# How does Matlab calculate Hausdorff distance?

## How does Matlab calculate Hausdorff distance?

% The Hausdorff distance between A and B, denoted by dH (A, B), is defined by: % dH (A, B)=max{sup dz(a,B), sup dz(b,A)}, for all a in A, b in B, % dH(A, B)

**How is Hausdorff distance calculated?**

In this example, h(Eq + 1, Oq) is larger than h(Eq + 1, Oq) and therefore the Hausdorff distance is equal to h(Eq + 1, Oq). Thus, for every model point o ∈ Oq the distance to the nearest edge pixel e ∈ Eq + 1 is calculated, and the maximum value is assigned to h(Oq, Eq + 1).

### What is Hausdorff distance used for?

Average Hausdorff distance is a widely used performance measure to calculate the distance between two point sets. In medical image segmentation, it is used to compare ground truth images with segmentations allowing their ranking.

**How do you read Hausdorff distance?**

The Hausdorff distance is the longest distance you can be forced to travel by an adversary who chooses a point in one of the two sets, from where you then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set.

## What is average Hausdorff distance?

**Is Hausdorff distance symmetric?**

Hausdorff Distance Image Comparison. The function h(A,B) is called the directed Hausdorff `distance’ from A to B (this function is not symmetric and thus is not a true distance). It identifies the point that is farthest from any point of B, and measures the distance from a to its nearest neighbor in B.

### How do you find the distance between two sets?

The distance between two sets C and D, in a norm ·, is defined as dist(C, D) = inf{x − y | x ∈ C, y ∈ D}.

**Is Hausdorff distance a metric?**

The function D(X, Y) is called the Hausdorff distance between sets X and Y. It is well known that D is a pseudometric on M and it is a complete metric on Mc.

## How is the distance formula correctly written?

The Distance Formula itself is actually derived from the Pythagorean Theorem which is {a^2} + {b^2} = {c^2} where c is the longest side of a right triangle (also known as the hypotenuse) and a and b are the other shorter sides (known as the legs of a right triangle).