Department of Image Processing

Nejprve bude stručné připomenutí metody grafů a metody získávání
afinních momentových invariantů jako řešení Cayleyovy - Aronholdovy
diferenciální rovnice. Dokazovaná věta pak zní: Každý afinní momentový
invariant získaný řešením rovnic lze vyjádřit jako lineární kombinaci
afinních momentových invariantů získaných metodou grafů. Na zápis
příslušné lineární kombinace se můžeme dívat jako na soustavu lineárních
rovnic, kde koeficienty lineární kombinace jsou neznámé a dokazujeme

Evaluation of symptoms on a plant is a simple mean of determining the progress of disease. For its speed and unnecessity of special equipment is the visual evaluation still a widely used method. It assesses disease symptoms by various scales and guides. But due to individual subjective evaluation this method does not fulfil requirements on accuracy and reproducibility. These deficits can be partially or fully eliminated by using methods of image processing.

The term cyclostationarity refers to a special class of signals which exhibit periodicity in their statistics. In this work, we focused on geometrical transformations and showed that images that have undergone such transformations contain hidden cyclostationary features. This justifies employing the well–developed theory of cyclostationarity and its efficient methods for analyzing images' history in respect to geometrical transformations.

Objectives

Recognition of partially occluded objects is an important task in a general 3D scene understanding. We focused our research to recognition of binary 2D objects with complicated curved boundary.

Precise invariants with respect to projective transformation of space coordinates

u = (a₀ + a₁x + a₂y)/(c₀ + c₁x + c₂y)
v = (b₀ + b₁x + b₂y)/(c₀ + c₁x + c₂y)

The affine transform is general linear transformation of space coordinates of the image:

u = a₀ + a₁x + a₂y
v = b₀ + b₁x + b₂y.

The affine moment invariants are features for pattern recognition computed from moments of objects on images that do not change their value in affine transformation. The geometric moment of order p + q of the image f is defined

.