在Matlab中过滤包含NaN的图像? [英] Filter image that contains NaNs in Matlab?
问题描述
我有一个表示某些数据的2d数组(doubles)，并且其中有一堆NaNs.数据的轮廓图如下所示:
I have a 2d array (doubles) representing some data, and it has a bunch of NaNs in it. The contour plot of the data looks like this:
所有白色空间均为NaNs，灰色菱形可供参考，填充轮廓显示了我数据的形状.当我用imfilt过滤数据时，NaNs会明显咀嚼到数据中，因此我们最终得到这样的结果:
All of the white spaces are NaNs, the gray diamond is there for reference, and the filled contour shows the shape of my data. When I filter the data with imfilt, the NaNs significantly chew into the data, so we end up with something like this:
您可以看到支撑架明显收缩.我无法使用它，因为它已经侵蚀了边缘上一些更有趣的变化(由于我的实验所特有的原因，这些边缘很重要).
You can see that the support set is significantly contracted. I can't use this, as it has chewed into some of the more interesting variations on the edges (for reasons specific to my experiments, those edges are important).
是否有一个功能可以在NaNs岛中进行过滤，该功能可以处理类似于矩形过滤窗口边缘的边缘，而不仅仅是杀死边缘?类似于nanmean函数，除了卷积图像之外?
Is there a function to filter within an island of NaNs that treats edges similar to edges of rectangular filtering windows, instead of just killing the edges? Sort of like an nanmean function, except for convolving images?
这是我的过滤器代码:
filtWidth = 7;
imageFilter=fspecial('gaussian',filtWidth,filtSigma);
%convolve them
dataFiltered = imfilter(rfVals,imageFilter,'symmetric','conv');
以及绘制轮廓图的代码:
and the code for plotting the contour plot:
figure
contourf(dataFiltered); hold on
plot([-850 0 850 0 -850], [0 850 0 -850 0], 'Color', [.7 .7 .7],'LineWidth', 1); %the square (limits are data-specific)
axis equal
Mathworks文件交换处有一些代码( ndanfilter.m )接近我想要的，但是我相信它只能对散布在图像内部上的NaNs进行插值，而不是显示这种岛型效果的数据.
There is some code at the Mathworks file exchange (ndanfilter.m) that comes close to what I want, but I believe it only interpolates NaNs that are sprinkled on the interior of an image, not data showing this island-type effect.
注意:我刚刚发现 nanconv.m ，它以一种非常直观的用法来实现我想要的功能(对图像进行卷积，忽略NaN，就像nanmean的作品一样).我已将此部分作为我接受的答案的一部分，并与其他答案的效果进行了比较.
Note: I just found nanconv.m, which does exactly what I want, with a very intuitive usage (convolve an image, ignoring NaN, much like nanmean works). I've made this part of my accepted answer, and include a comparison to the performance of the other answers.
相关问题
推荐答案
The technique I ended up using was the function nanconv.m at Matlab's File Exchange. It does exactly what I was looking for: it runs the filter in a way that ignores the NaNs just the way that Matlab's built-in function nanmean does. This is a hard to decipher from the documentation of the function, which is a tad cryptic.
这是我的用法:
filtWidth = 7;
filtSigma = 5;
imageFilter=fspecial('gaussian',filtWidth,filtSigma);
dataFiltered = nanconv(data,imageFilter, 'nanout');
我要在下面粘贴nanconv函数(
I'm pasting the nanconv function below (it is covered by the BSD license). I will post images etc when I get a chance, just wanted to post what I ended up doing for anyone curious about what I did.
与其他答案的比较
使用 gnovice的解决方案结果直观上看非常好，但是边缘上存在一些定量的斑点.实际上，将图像外推到边缘会导致我的数据边缘出现许多虚假的高值.
Using gnovice's solution the results look intuitively very nice, but there are some quantitative blips on the edges that were a concern. In practice, the extrapolation of the image beyond the edges led to many spuriously high values at the edges of my data.
使用 krisdestruction的建议用原始数据替换丢失的位，看起来也很不错(尤其是对于非常小的过滤器)，但是(根据设计)您最终会在边缘得到未过滤的数据，这对我的应用程序来说是个问题.
Using krisdestruction's suggestion of replacing the missing bits with the original data, also looks pretty decent (especially for very small filters), but (by design) you end up with unfiltered data at the edges, which is a problem for my application.
nanconv
function c = nanconv(a, k, varargin)
% NANCONV Convolution in 1D or 2D ignoring NaNs.
% C = NANCONV(A, K) convolves A and K, correcting for any NaN values
% in the input vector A. The result is the same size as A (as though you
% called 'conv' or 'conv2' with the 'same' shape).
%
% C = NANCONV(A, K, 'param1', 'param2', ...) specifies one or more of the following:
% 'edge' - Apply edge correction to the output.
% 'noedge' - Do not apply edge correction to the output (default).
% 'nanout' - The result C should have NaNs in the same places as A.
% 'nonanout' - The result C should have ignored NaNs removed (default).
% Even with this option, C will have NaN values where the
% number of consecutive NaNs is too large to ignore.
% '2d' - Treat the input vectors as 2D matrices (default).
% '1d' - Treat the input vectors as 1D vectors.
% This option only matters if 'a' or 'k' is a row vector,
% and the other is a column vector. Otherwise, this
% option has no effect.
%
% NANCONV works by running 'conv2' either two or three times. The first
% time is run on the original input signals A and K, except all the
% NaN values in A are replaced with zeros. The 'same' input argument is
% used so the output is the same size as A. The second convolution is
% done between a matrix the same size as A, except with zeros wherever
% there is a NaN value in A, and ones everywhere else. The output from
% the first convolution is normalized by the output from the second
% convolution. This corrects for missing (NaN) values in A, but it has
% the side effect of correcting for edge effects due to the assumption of
% zero padding during convolution. When the optional 'noedge' parameter
% is included, the convolution is run a third time, this time on a matrix
% of all ones the same size as A. The output from this third convolution
% is used to restore the edge effects. The 'noedge' parameter is enabled
% by default so that the output from 'nanconv' is identical to the output
% from 'conv2' when the input argument A has no NaN values.
%
% See also conv, conv2
%
% AUTHOR: Benjamin Kraus (bkraus@bu.edu, ben@benkraus.com)
% Copyright (c) 2013, Benjamin Kraus
% $Id: nanconv.m 4861 2013-05-27 03:16:22Z bkraus $
% Process input arguments
for arg = 1:nargin-2
switch lower(varargin{arg})
case 'edge'; edge = true; % Apply edge correction
case 'noedge'; edge = false; % Do not apply edge correction
case {'same','full','valid'}; shape = varargin{arg}; % Specify shape
case 'nanout'; nanout = true; % Include original NaNs in the output.
case 'nonanout'; nanout = false; % Do not include NaNs in the output.
case {'2d','is2d'}; is1D = false; % Treat the input as 2D
case {'1d','is1d'}; is1D = true; % Treat the input as 1D
end
end
% Apply default options when necessary.
if(exist('edge','var')~=1); edge = false; end
if(exist('nanout','var')~=1); nanout = false; end
if(exist('is1D','var')~=1); is1D = false; end
if(exist('shape','var')~=1); shape = 'same';
elseif(~strcmp(shape,'same'))
error([mfilename ':NotImplemented'],'Shape ''%s'' not implemented',shape);
end
% Get the size of 'a' for use later.
sza = size(a);
% If 1D, then convert them both to columns.
% This modification only matters if 'a' or 'k' is a row vector, and the
% other is a column vector. Otherwise, this argument has no effect.
if(is1D);
if(~isvector(a) || ~isvector(k))
error('MATLAB:conv:AorBNotVector','A and B must be vectors.');
end
a = a(:); k = k(:);
end
% Flat function for comparison.
o = ones(size(a));
% Flat function with NaNs for comparison.
on = ones(size(a));
% Find all the NaNs in the input.
n = isnan(a);
% Replace NaNs with zero, both in 'a' and 'on'.
a(n) = 0;
on(n) = 0;
% Check that the filter does not have NaNs.
if(any(isnan(k)));
error([mfilename ':NaNinFilter'],'Filter (k) contains NaN values.');
end
% Calculate what a 'flat' function looks like after convolution.
if(any(n(:)) || edge)
flat = conv2(on,k,shape);
else flat = o;
end
% The line above will automatically include a correction for edge effects,
% so remove that correction if the user does not want it.
if(any(n(:)) && ~edge); flat = flat./conv2(o,k,shape); end
% Do the actual convolution
c = conv2(a,k,shape)./flat;
% If requested, replace output values with NaNs corresponding to input.
if(nanout); c(n) = NaN; end
% If 1D, convert back to the original shape.
if(is1D && sza(1) == 1); c = c.'; end
end
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