AAMToolbox viewing one population in shape space: Difference between revisions
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[[Tutorials on the Shape modelling toolbox#1|Back to Tutorial pages]]<br> | [[Tutorials on the Shape modelling toolbox#1|Back to Tutorial pages]]<br> | ||
=<span style="color:Navy;">'''What''' is Shape Space?</span>= | =<span style="color:Navy;">'''What''' is Shape Space?</span>= | ||
===<span style="color:FireBrick;">Mean shape</span>=== | ===<span style="color:FireBrick;">Mean shape</span>=== | ||
{| border="0" cellpadding="5" cellspacing="3" | {| border="0" cellpadding="5" cellspacing="3" | ||
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Each '''spot''' represents one of the''' input point models''' (images).<br><br> | Each '''spot''' represents one of the''' input point models''' (images).<br><br> | ||
Each point model represents 38 points i.e. 38*2=76 values in the normal two dimensional viewing space OR a single point in 72 dimensional space. However, we cannot visualise 78 dimensional space so we have used PCA to choose a view point (a rotation of the space) such that we can see the two principle components. This allows us to visualise and '''focus on the significant (in the sense of accounting for the most variance) parameters'''. Of course, it might be another component that is most significant in biological terms. It is also quite possible that the biologically important parameters are correlated non-linearly in which case they could be invisible in this project because they are distributed into the new components as awkwardly as they were in the original data. | Each point model represents 38 points i.e. 38*2=76 values in the normal two dimensional viewing space OR a single point in 72 dimensional space. However, we cannot visualise 78 dimensional space so we have used PCA to choose a view point (a rotation of the space) such that we can see the two principle components. This allows us to visualise and '''focus on the significant (in the sense of accounting for the most variance) parameters'''. Of course, it might be another component that is most significant in biological terms. It is also quite possible that the biologically important parameters are correlated non-linearly in which case they could be invisible in this project because they are distributed into the new components as awkwardly as they were in the original data. | ||
|width="400pt"|[[File:Cartoons_shape_space_1_AAMToolbox.png|400px|Shape space]]<br>Shape Space: the principle component is plotted on the x-axis (abscissa) and the component that accounts for the second largest amount of variation is plotted on the y-axis (ordinate). Pink diamond shows the position of the mean shape. The other points | |width="400pt"|[[File:Cartoons_shape_space_1_AAMToolbox.png|400px|Shape space]]<br>Shape Space: the principle component is plotted on the x-axis (abscissa) and the component that accounts for the second largest amount of variation is plotted on the y-axis (ordinate). Pink diamond shows the '''position of the mean shape'''. The other points | ||
|} | |} | ||
===<span style="color:FireBrick;">Exploring the data in shape space</span>=== | =<span style="color:Navy;">'''How''' do we view shape space?</span>= | ||
=<span style="color:Navy;">Exploring further.</span>= | |||
===<span style="color:FireBrick;">Exploring the data in shape space, '''where are the samples'''?</span>=== | |||
{| border="0" cellpadding="5" cellspacing="3" | {| border="0" cellpadding="5" cellspacing="3" | ||
|- valign="top" | |- valign="top" | ||
|width=" | |width="200pt"|Each''' pink '''circle marker represents a data sample''''''. Right clicking on a marker opens a context menu. Here we have selected to view the associated original image and its point model (shown to the left). <br><br> | ||
Showing the PC values causes them to be echoed to the command window.<br><br> | Showing the PC values causes them to be echoed to the command window.<br><br> | ||
|width=" | |width="400pt"|[[File:Cartoons_shape_space_2_AAMToolbox.png|400px|Shape space]]<br>Shape Space context menu for the markers. The top-left sample has been selected and the associated image/point model is shown on the left. | ||
|} | |} | ||
===<span style="color:FireBrick;">'''What is the '''distance''' between samples'''?</span>=== | |||
{| border="0" cellpadding="5" cellspacing="3" | {| border="0" cellpadding="5" cellspacing="3" | ||
|- valign="top" | |- valign="top" | ||
|width=" | |width="200pt"|Right clicking on a marker opens a context menu. Here we have selected to view the '''distance between the two''' visible markers. The distances (and squared distances) for each of the components is shown in the right. <br><br> | ||
Showing the PC values causes them to be echoed to the command window.<br><br> | Showing the PC values causes them to be echoed to the command window.<br><br> | ||
|width=" | |width="400pt"|[[File:Cartoons_shape_space_3_AAMToolbox.png|400px|Shape space]]<br>Shape Space: '''distance between two points'''. | ||
|} | |||
===<span style="color:FireBrick;">Can we '''interpolate''' between samples?</span>=== | |||
{| border="0" cellpadding="5" cellspacing="3" | |||
|- valign="top" | |||
|width="200pt"|Here we have selected to add a 'vector' (arrow) between one point and another.<br><br> | |||
Click on the Vectors button in the Shape Space Viewer interface and the vector will be displayed as an arrow. Click on a sequence of samples to create a path through shape space.<br><br> | |||
|width="400pt"|[[File:Walk_through_shape_space_AAMToolbox.png|400px|Shape space]]<br>Shape Space: '''distance between two points'''. | |||
|} | |} |