Documentation>vl_demo_frame

# Source code for ``vl_demo_frame.m

This file is located in the ``toolbox/demo folder in VLFeat package.

    % VL_DEMO_FRAME  Demonstrates vl_plotframe and vl_frame2oell

    %% A standard frame is a unit circle centered at the origin with a
    % radius pointing in the positive Y direction. Since images use a
    % left-handed coordinate system (X axis pointing right, Y axis
    % pointing downwards), the radius will point downwards.

    A = eye(2) ;
    T = [0;0] ;

    figure(1) ; clf ;
    vl_plotframe([T ; A(:)], 'b', 'linewidth', 5) ; hold on ;

    % The same frame can be specified as 4 numbers: translation, scale
    % (unit), and rotation (zero).
    vl_plotframe([T ; 1 ; 0]) ;

    axis equal ; set(gca,'ydir','reverse') ; grid on ;
    vl_figaspect(1) ;
    vl_demo_print(1, 'frame_standard') ;

    %% A positive rotation is appears clockwise in the standard image
    % reference frame.

    angle = pi/4 ;
    R = [cos(angle), -sin(angle) ; sin(angle) cos(angle)] ;
    A = R ;

    figure(2) ; clf ;
    vl_plotframe([T ; A(:)], 'b', 'linewidth', 5) ; hold on ;

    % The same frame can be specified as 4 numbers: translation, scale and
    % rotation.
    vl_plotframe([T ; 1 ; angle]) ;

    axis equal ; set(gca,'ydir','reverse') ; grid on ;
    vl_figaspect(1) ;
    vl_demo_print(2, 'frame_rotated') ;

    %% A more complex example, involving a generic affine
    % frame. The frame is the result of applying a given affine
    % transformation to the standard frame.

    angle = pi/4 ;
    R = [cos(angle), -sin(angle) ; sin(angle) cos(angle)] ;
    S = [1 0 ; 0 .5] ;
    A = R*S*R ;

    figure(3) ; clf ;
    vl_plotframe([T ; A(:)], 'b', 'linewidth', 3) ; hold on ;

    axis equal ; set(gca,'ydir','reverse') ; grid on ;
    vl_figaspect(1) ;
    vl_demo_print(3, 'frame_affine') ;

    %% An oriented ellipse can be easily transformed in an unoriented
    % one by removing the orientation. The opposite transformation is
    % possible as well, provided that a conventional orientation is
    % assigned to it.

    clear frames1 frames2 ;
    randn('state',0) ;
    rand('state',0) ;
    for i = 1 : 5
      % sample a random ellipse
      angle1 = rand * 2*pi;
      angle2 = rand * 2*pi;
      R1 = [cos(angle1), -sin(angle1) ; sin(angle1) cos(angle1)] ;
      R2 = [cos(angle2), -sin(angle2) ; sin(angle2) cos(angle2)] ;
      A = 0.3*R1*diag(rand(2,1)+0.5)*R2 ;
      frames1(:,i) = [i ; 0 ; A(:)] ;

      % get the unoriented variant of the same ellipse
      S = A*A' ;
      frames2(:,i) = [i ; 0 ; S(1,1) ; S(1,2) ; S(2,2)] ;
    end

    % Recover oriented ellipses from the unoriented ones; note that
    % vl_frame2oell assigns all frames an upright orientation.

    frames3 = vl_frame2oell(frames2) ;

    frames1(2,:) = 0 ;
    frames2(2,:) = 1 ;
    frames3(2,:) = 2 ;

    figure(4) ; clf ;
    vl_plotframe(frames1,'r') ;
    vl_plotframe(frames2,'g') ;
    vl_plotframe(frames3,'b') ;

    axis equal tight ; set(gca,'ydir','reverse') ; grid on ;
    vl_figaspect(5/3) ;
    vl_demo_print(4, 'frame_frame2oell') ;