Operators

# derivate_vector_field (Operator)

## Name

derivate_vector_field — Convolve a vector field with derivatives of the Gaussian.

## Signature

derivate_vector_field(VectorField : Result : Sigma, Component : )

## Description

derivate_vector_field convolves the components of a vector field with the derivatives of a Gaussian and calculates various features derived therefrom. derivate_vector_field only accepts vector fields of the semantic type 'vector_field_relative'. The VectorField F(r,c)=(u(r,c),v(r,c)) is defined as in optical_flow_mg. Sigma is the parameter of the Gaussian (i.e., the amount of smoothing). If a single value is passed in Sigma, the amount of smoothing in the column and row direction is identical. If two values are passed in Sigma, the first value specifies the amount of smoothing in the column direction, while the second value specifies the amount of smoothing in the row direction. The possible values for Component are:

'curl':

The curl of the vector field. One application of using 'curl' is to analyse optical flow fields. Metaphorically speaking, the curl is how much a small boat would rotate if the vector field was a fluid.

'divergence':

The divergence of the vector field. One application of using 'divergence' is to analyze optical flow fields. Metaphorically speaking, the divergence is where the source and sink would be if the vector field was a fluid.

When used in context of photometric stereo, the operator derivate_vector_field offers two more parameters, which are especially designed to process the gradient field that is returned by photometric_stereo. In this case, we interpret the input vector field as gradient of the underlying surface.

In the following formulas, the input vector field is therefore noted as

where the first and second component of the input is the gradient field of the surface f(r,c). In the formulas below f_rc denotes the first derivative in column direction of the first component of the gradient field.

'mean_curvature':

Mean curvature H of the underlying surface when the input vector field VectorField is interpreted as gradient field. One application of using 'mean_curvature' is to process the vector field that is returned by photometric_stereo. After filtering the vector field, even tiny scratches or bumps can be segmented.

'gauss_curvature':

Gaussian curvature K of the underlying surface when the input vector field VectorField is interpreted as gradient field. One application of using 'gauss_curvature' is to process the vector field that is returned by photometric_stereo. After filtering the vector field, even tiny scratches or bumps can be segmented. If the underlying surface of the vector field is developable, the Gaussian curvature is zero.

## Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on domain level.
• Automatically parallelized on tuple level.

## Parameters

VectorField (input_object)  singlechannelimage(-array) object (vector_field)

Input vector field.

Result (output_object)  singlechannelimage(-array) object (real)

Filtered result images.

Sigma (input_control)  real(-array) (real)

Sigma of the Gaussian.

Default value: 1.0

Suggested values: 0.7, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0

Typical range of values: 0.2 ≤ Sigma ≤ 50.0

Restriction: 0.01 <= Sigma <= 50.0

Component (input_control)  string (string)

Component to be calculated.

Default value: 'mean_curvature'

List of values: 'curl', 'divergence', 'gauss_curvature', 'mean_curvature'

## Result

If the parameters are valid, the operator derivate_vector_field returns the value 2 (H_MSG_TRUE). The behavior in case of empty input (no input images available) is set via the operator set_system('no_object_result',<Result>). If necessary, an exception is raised.

## Module

Foundation

 Operators