Difference between revisions of "Descriptor Proposed JFMR"
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| − | The implementation of a descriptor that use the phase portrait depends of the components <math>u</math> and <math>v</math> obtained of the simulation that allow to construct the equation system, although needed the gradient of <math>u</math> and <math>v</math> to construct the system. With the system, we can calculate the determinant and the trace and can calculate <math>\lambda</math> | + | The implementation of a descriptor that use the phase portrait depends of the components <math>u</math> and <math>v</math> obtained of the simulation that allow to construct the equation system, although needed the gradient of <math>u</math> and <math>v</math> to construct the system. With the system, we can calculate the determinant and the trace and can calculate <math>\lambda</math> using the next formula: |
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| + | <math> \lambda_1,\lambda_2 = 0.5 (Trace(A) \pm \sqrt{Trace(A)^2 - 4det(A)})</math> | ||
Revision as of 19:35, 19 September 2015
Definition
Given a vector field 
, where 
and 
represent the components of the winds of each of the annotations.
The vector field representation allow to observe the behavior of the winds in a determined region, these behavior are represented as:
- Vortex
- Confluence
- Difluence
- Saddle Point
The meteorologists annotated the different configurations that it can present in a period of time and a level determined, this process was done with an annotations tool that allow to select this configurations.
Model Mathematic
Given a vector field 
, a way to classify this configurations is through the use of phase portrait, this method is used in the dynamic system to understand the behavior of functions of 2 or more variables. In computer vision is used in the detection corner, mammography and others.
This method allows to construct a equation system in which these can calculate the determinant and the trace.
The trace and the determinant indicate as is the behavior of the system. To calculate the trace and determinant with their:
Implementation
The implementation of a descriptor that use the phase portrait depends of the components and obtained of the simulation that allow to construct the equation system, although needed the gradient of and to construct the system. With the system, we can calculate the determinant and the trace and can calculate 
using the next formula:
