# 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).