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Hello can someone explain the semantical meaning of the structure tensor and the Hessian matrix. I am aware of how it is calculated, but i find it difficult to comprehend what they describe in the image and how they can be used to detect corners (Harris) and detect Blobs (SURF).

Any help is greatly appreciated, thank you in advance.

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The structure tensor consists of first derivatives of the image. If the first derivative is high in one particular direction (one large eigenvalue of the structure tensor), then you have an edge. It the first derivative is high in two directions (two large eigenvalues), then you have a corner.

The Hessian matrix consists of second derivatives. Think of the Laplacian. It is the trace of the Hessian, and it is a center-surround filter, which gives you a high absolute value for a bright blob surrounded by dark background or vice versa. That's why it is blob detector.

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