User:Paulbrookes/sandbox

The Man With the Stick
The Man With the Stick is a recurring character on the TV show Vic Reeves Big Night Out. He is played by Bob Mortimer.

In the show, presenter Vic Reeves would read out drawings on The Man With the Stick’s helmet, outlining what he had investigated that week. In some episodes he would reveal an object on the end of the stick, usually at the end of the show.

Shape Texture Based on Sub-Objects
Object Features > Texture > Shape Texture Based on Sub-Objects

Shape Texture Based on Sub-Objects features refer to the shape of sub-objects. To use these features successfully we recommend an accurate segmentation of the map to ensure sub-objects are as meaningful as possible. To refer to an image object level of sub-objects, you can edit the level distance.

Area of Sub-Objects: Mean
Object Features > Texture > Shape Texture Based on Sub-Objects > Area of Sub-Objects: Mean

Mean value of the areas of the sub-objects.

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$\#P_u$$ is the total number of pixels contained in $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle \frac{1}{\# S_v (d)} \sum_{ \epsilon S_v (d)} \#P_u$$

Feature Value Range
$$[0, {\mathrm {scene \ size}}]$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Area of Sub-Objects: Std. Dev.
Object Features > Texture > Shape Texture Based on Sub-Objects > Area of Sub-Objects: Std Dev.

Standard deviation of the areas of the sub-objects.

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$P_u$$ is the total number of pixels contained in $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle\sqrt{\frac{1}{\#S_v(d)} \left(\sum_{u \epsilon S_v\left(d\right)} \#P^2_u - \frac {1}{\#S_v\left(d\right)} \sum_{u \epsilon S_v\left(d\right)} \#P_u \sum_{u \epsilon S_v\left(d\right)} \#P_u \right)}$$

Feature Value Range
$$[0, {\mathrm {scene \ size}}]$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Density of Sub-Objects: Mean
Object Features > Texture > Shape Texture Based on Sub-Objects > Density of Sub-Objects: Mean

Mean value calculated from the densities of the sub-objects.

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$a(u)$$ is the density of $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle \frac{1}{\# S_v (d)} \sum_{ u \epsilon S_v (d)} a(u)$$

Feature Value Range
$$[0, {\mathrm {depending \ on \ image \ object \ shape}]}$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Density of Sub-Objects: Std. Dev.
Object Features > Texture > Shape Texture Based on Sub-Objects > Density of Sub-Objects: Stddev.

Standard deviation calculated from the densities of the sub-objects.

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$a(u)$$ is the density of $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle\sqrt{\frac{1}{\#S_v(d)} \left(\sum_{u \epsilon S_v\left(d\right)} a^2(u) - \frac {1}{\#S_v\left(d\right)} \sum_{u \epsilon S_v\left(d\right)} a(u) \sum_{u \epsilon S_v\left(d\right)} a(u) \right)}$$

Feature Value Range
$$[0, {\mathrm {depending \ on \ image \ object \ shape}}]$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Asymmetry of Sub-Objects: Mean
Object Features > Texture > Shape Texture Based on Sub-Objects > Asymmetry of Sub-Objects: Mean

Mean value of the asymmetries of the sub-objects.

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$a(u)$$ is the asymmetry of $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle \frac{1}{\# S_v (d)} \sum_{ u \epsilon S_v (d)} a(u)$$

Feature Value Range
$$[0, {\mathrm {depending \ on \ image \ object \ shape}]}$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Asymmetry of Sub-Objects: Std. Dev.
Object Features > Texture > Shape Texture Based on Sub-Objects > Asymmetry of Sub-Objects: Stddev.

Standard deviation of the asymmetries of the sub-objects.

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$a(u)$$ is the asymmetry of $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle \frac{1}{\# S_v (d)} \sum_{ u \epsilon S_v (d)} a(u)$$

Feature Value Range
$$[0, {\mathrm {depending \ on \ image \ object \ shape}]}$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Direction of Sub-Objects: Mean
Object Features > Texture > Shape Texture Based on Sub-Objects > Direction of Sub-Objects: Mean

The mean value of the directions of the sub-objects. In the computation, the directions are weighted with the asymmetry of the respective sub-objects. The more asymmetric an image object, the more significant its main direction.

Before computing the actual feature value, the algorithm compares the variance of all sub-object main directions with the variance of the sub-object main directions, where all directions between 90° and 180° are inverted. The set of sub-object main directions which has the lower variance is selected for the calculation of the main direction mean value, weighted by the sub-object asymmetries.

%center%Attach:XDRef/DirectionOfSubobjects_Mean_Fe.png | For calculation, the directions between 90° and 180° are inverted, which means the direction is reduced by 180°

Parameters

 * $$S_v(d)$$ is the sub-object of an image object $$v$$ at distance $$d$$
 * $$a(u)$$ is the main direction of $$u$$
 * $$d$$ is the image object level distance

Expression
$$\displaystyle \frac{1}{\# S_v (d)} \sum_{ u \epsilon S_v (d)} a(u)$$

Feature Value Range
$$[0^{\circ}, 180^{\circ}]$$

Condition
If $$S_v(d)= \varnothing \therefore$$ the formula is invalid.

Direction of Sub-Objects: Std. Dev.
Object Features > Texture > Shape Texture Based on Sub-Objects > Direction of Sub-Objects: Stddev

Standard deviation of the directions of the sub-objects. Similar to Direction of Sub-Objects: Mean feature, the sub-object main directions are weighted by the asymmetries of the respective sub-objects. The set of sub-object main directions from which the standard deviation is calculated is determined in the same way.