我是计算机视觉的新手，在浏览光流主题时，我有一个概念上的怀疑。 为什么不能通过取两个连续帧中像素的x和y值之间的差异并将它们除以两帧之间的时间来计算光流量？ 例如，图像中的像素在2个连续帧中从（0,0）移动到（1,1），其可以使用亮度恒定性假设来匹配。通过了解帧率，你可以找到你和v。
答案 0 :(得分：1)
通过查看http://en.m.wikipedia.org/wiki/Optical_flow
中的估算部分，您可以在数学上看到它不受约束这被称为光圈问题。您可以在此处进行谷歌搜索以获取更多讨论，或参阅http://en.m.wikipedia.org/wiki/Motion_perception#The_aperture_problem获取动画示例。
答案 1 :(得分：0)
我用引用here回答了这个问题，然后将其删除，因为它只是一个链接。我分享这段代码的原因是因为它提供了一种交互式方式来获得关于孔径问题的直觉。我提供链接的原因是因为代码大小...但是如果这是编辑者想要它的方式，那么就这样，在这条消息的末尾找到整个函数。在Matlab中最简单地使用函数：
ApertureIllustration;
...我想用链接分享的完整尺码：
% Author: Stefan Karlsson, Josef Bigun, 2014
function ApertureIllustration(type)
%interactive visualization of the aperture problem in optical flow
%estimation. This script animates a pattern of horizontal smooth bars within
% the support of a large disk. The pattern is in a circular motion pattern.
% a smaller apperture is present in the middle of the image. The
% only view the user gets is through the aperture, except for a periodic
% reveal of the scene
% input "type":
% 'regular' , [default] circular aperture, single motion
% 'barber' , rectangular aperture, barberpole illusion
% 'multiple', circular aperture, multiple motions
% 'color' , circular aperture, multiple motions in seperate color channels
%%%%%%%%%%%%
% The script supports the following interface:
% MOUSE:
% click to enable mouse move of aperture, mouse scroll to change aperture
% radius
% KEYBOARD:
% Arrow Keys: move the aperture around
% Q/A : Radius of the aperture
% W/S : the fuzziness of the boundary(higher values makes it Gaussian-like)
%%%%%%%
if nargin < 1
type = 'regular';end
if ~isnumeric(type)
switch lower(type)
case 'regular'
type = 1;
case 'barber'
type = 2;
case 'multiple'
type = 3;
case 'color'
type = 4;
end
end
%widht and height of the image
w = 250;
h = 250;
innerRadius = 0.3; %initial radius of aperture
%initial position of aperture, x and y:
innerPx = 0;
innerPy = 0;
minFuz = 0.01;
%initial fuzziness of aperture:
if type == 2
innerFuz = minFuz;
else
innerFuz = 1/10;
end
fuz = 1/20; %fuzziness of the moving pattern
%limits in the image are in [-1,+1] for both x and y:
xlims = linspace(-1,1,w);
ylims = linspace(-1,1,h);
[x,y] = meshgrid(xlims,ylims);
p = linspace(0,2*pi,200); %used for painting the red boundary of aperture
%When linesmoothing option is on, there is a small bug in the offset of the
%position of linesegments. Fix this with the following added values
bugXVal = (xlims(2)-xlims(1))/2;
bugYVal = (ylims(2)-ylims(1))/2;
%keep track of mouse clicked:
bHasClicked = 0;
%create figure, set up callback functions:
hFig = figure('WindowKeyPressFcn',@localKeyFunc,...
'WindowButtonDownFcn', @localMousepress);
hold on
%create the graphics objects, store handles
if type < 4
hIm = imagesc(xlims, ylims,x,[0,1]);colormap gray(256);
else
hIm = imagesc(xlims, ylims,zeros([size(x),3]));
end
if type ~= 2
hCirc = plot(innerRadius*sin(p)-innerPx,innerRadius*cos(p)-innerPy,...
'color',[0.6 0.2 0.2],'LineSmoothing','on');
end
axis off;axis image;
t = 0; %simulation time
tInc = 0.1; %time increment, simulation
targetFramerate = 15; %target framerate, in real-world time
%as long as the user hasnt shut down the figure, loop:
while ishandle(hFig)
tic; %time every iteration to control framerate
%screener will hold the "characterisitc function" of the aperture:
if type ~= 2
screener = sig((innerRadius-0.01)-sqrt((x-innerPx).^2+(y-innerPy).^2),innerFuz);
else
screener = sig(x-innerPx+innerRadius,innerFuz).*sig(-(x-innerPx-innerRadius),innerFuz).*...
sig(y-innerPy+innerRadius*2 ,innerFuz).*sig(-(y-innerPy-innerRadius*2 ),innerFuz);
end
t = t+ tInc;
%the update equation: sigmoidal function for disk boundaries,
%trigonometric tricks for slowly varying bars
%centre of the moving pattern is at (cX,xY)
if type <= 2
cX = 0.15*cos(t);
cY = 0.15*sin(t);
else % type > = 3
cX = 0;
cY = 0.15*sin(t);
end
if type < 4
im = sig(0.84^2-(x-cX).^2-(y-cY).^2,fuz).*(cos(40*(sin(t/100)*(x-cX)+cos(t/100)*(y-cY)))+1)/2;
else
im(:,:,2) = sig(0.84^2-(x-cX).^2-(y-cY).^2,fuz).*(cos(40*(sin(t/100)*(x-cX)+cos(t/100)*(y-cY)))+1)/2;
end
if type > 2
t2 = -t-100*pi/2;
% t2 = t;
cX = 0.15*cos(t);
cY = 0;
% cX = 0.15*cos(t2); %centre of the moving pattern is at (cX,xY)
% cY = 0.15*sin(t2);
if type ==3
% newIm = (newIm + backWeight*(250-newIm).*(iix>0)); %apply the background, fixed with hard boundary
im = (im + 0.7*ed(im).*(1-im).*...
sig(0.84^2-(x-cX).^2-(y-cY).^2,fuz).*(cos(40*(sin(t2/100)*(x-cX)+cos(t2/100)*(y-cY)))+1)/2);
else %type ==4
im(:,:,3) = (1-im(:,:,2)).*...
sig(0.84^2-(x-cX).^2-(y-cY).^2,fuz).*(cos(40*(sin(t2/100)*(x-cX)+cos(t2/100)*(y-cY)))+1)/2;
end
end
%alpha is used for the periodical unveiling of the full motion pattern
if type <=2
alpha = max(min(((-0.8- 1.55*sin(t*0.35))/2), 0.35),0);
else % type >=3
alpha = max(min(((1.5- 1.55*sin((t+45*tInc)*0.25))/2), 0.35),0);
end
if type < 4
if type == 2
im = alpha*im + (1-alpha)*(screener.*im + (1 - screener)/2);
else
im = alpha*im + (1-alpha)*screener.*im;
end
else
im = alpha*im + (1-alpha)*bsxfun(@times,screener,im);
end
%update graphics:
set(hIm,'CData',im);
if type ~= 2
set(hCirc,'XData',(innerRadius-bugXVal)*sin(p)+innerPx+bugXVal, ...
'YData',(innerRadius-bugYVal)*cos(p)+innerPy+bugYVal);
end
%restrict frame rate:
timeToSpare = (1/targetFramerate) - toc;
pause( max(timeToSpare , 1/100) );
end
%%%%%% nested helper functions
% sigmoidal function for fuzzy rendering:
function out=sig(x,fuzziness)
if (fuzziness == 0)
out = x > 0;
else
out= (1+erf(x./fuzziness))/2;
end
end
%%% keyboard event handler, callback function
function localKeyFunc(~,evnt)
switch evnt.Key,
case 'q', innerRadius = innerRadius +0.01;
case 'a', innerRadius = max(innerRadius -0.01,0.06);
case 'w', innerFuz = innerFuz +0.005;
case 's', innerFuz = max(innerFuz -0.005,minFuz);
case 'downarrow' , innerPy = max(-1,innerPy -0.02);
case 'uparrow' , innerPy = min(1,innerPy +0.02);
case 'rightarrow', innerPx = min(1,innerPx +0.02);
case 'leftarrow' , innerPx = max(-1,innerPx -0.02);
end
end
%%%mouse press event handler
function localMousepress(~,~)
mousePos=get(gca,'CurrentPoint');
if max(max(abs(mousePos(1,:))))<1.1
innerPy = mousePos(1,2);
innerPx = mousePos(1,1);
if ~bHasClicked
set (hFig, 'WindowButtonMotionFcn', @mouseMove,'WindowScrollWheelFcn',@mouseScroll);
bHasClicked = 1;
else
set (hFig, 'WindowButtonMotionFcn', '','WindowScrollWheelFcn','');
bHasClicked = 0;
end
end
end
%%%mouse scroll event handler, activated on click
function mouseScroll(~,callbackdata)
innerRadius = max(innerRadius +0.02*callbackdata.VerticalScrollCount,0.06);
end
%%%mouse move event handler, activated on click
function mouseMove (~, ~)
mousePos=get(gca,'CurrentPoint');
if max(max(abs(mousePos(1,:))))<1.1
innerPy = mousePos(1,2);
innerPx = mousePos(1,1);
end
end
% shadowing function for object partial occlusion. Based on the gradient
% magnitude, not physically justified, just a visualization hack really.
function out = ed(f)
gg = [0.2163, 0.5674, 0.2163];
dx = f(:,[ 2:end end ] ) - f(:,[1 1:(end-1) ] ) ;
dx = conv2(dx,gg' ,'same');
dy = f( [ 2:end end ],:) - f( [1 1:(end-1) ],:);
dy = conv2(dy,gg,'same');
out = ((dx.^2 + dy.^2)/8+1).^(-25);
end
end