一、matlab下圖像添加噪聲
clear all;
close all;
pt = '.\jp2k\';
ext = '*.bmp';
dis = dir([pt ext]);
nms = {dis.name};
for k = 1:1:length(nms)
nm = [pt nms{k}];
image = imread(nm);
g=imnoise(image,'gaussian',0.1,0.02); %加入高斯噪聲
imwrite(g, strcat('./noise/pic_',num2str(k),'.bmp'));
% 對圖像image進行相關操作
% G[nm]=imnoise(t,'gaussian',0.1,0.002); %加入高斯噪聲
end
二、待訓練圖像預處理
here are four common forms of data preprocessing a data matrix X, where we will assume that X is of size [N x D] (N is the number of data, D is their dimensionality).
1、Mean subtraction is the most common form of preprocessing. It involves subtracting the mean across every individual feature in the data, and has the geometric interpretation of centering the cloud of data around the origin along every dimension. In numpy, this operation would be implemented as: X -= np.mean(X, axis = 0). With images specifically, for convenience it can be common to subtract a single value from all pixels (e.g. X -= np.mean(X)), or to do so separately across the three color channels.
2、Normalization refers to normalizing the data dimensions so that they are of approximately the same scale. There are two common ways of achieving this normalization. One is to divide each dimension by its standard deviation, once it has been zero-centered: (X /= np.std(X, axis = 0)). Another form of this preprocessing normalizes each dimension so that the min and max along the dimension is -1 and 1 respectively. It only makes sense to apply this preprocessing if you have a reason to believe that different input features have different scales (or units), but they should be of approximately equal importance to the learning algorithm. In case of images, the relative scales of pixels are already approximately equal (and in range from 0 to 255), so it is not strictly necessary to perform this additional preprocessing step.
(用於將不同幅值範圍的數字歸一化到相同尺度，但是圖像[0~255]是沒必要歸一化的。)
Common data preprocessing pipeline. Left: Original toy, 2-dimensional input data. Middle: The data is zero-centered by subtracting the mean in each dimension. The data cloud is now centered around the origin. Right: Each dimension is additionally scaled by its standard deviation. The red lines indicate the extent of the data - they are of unequal length in the middle, but of equal length on the right.
——————————————————————————————————————————————————————
3、PCA and Whitening is another form of preprocessing. In this process, the data is first centered as described above. Then, we can compute the covariance matrix that tells us about the correlation structure in the data:
# Assume input data matrix X of size [N x D]
X -= np.mean(X, axis = 0) # zero-center the data (important)
cov = np.dot(X.T, X) / X.shape[0] # get the data covariance matrix
The (i,j) element of the data covariance matrix contains the covariance between i-th and j-th dimension of the data. In particular, the diagonal of this matrix contains the variances. Furthermore, the covariance matrix is symmetric and positive semi-definite. We can compute the SVD factorization of the data covariance matrix:
U,S,V = np.linalg.svd(cov)
where the columns of U are the eigenvectors and S is a 1-D array of the singular values. To decorrelate the data, we project the original (but zero-centered) data into the eigenbasis:
Xrot = np.dot(X, U) # decorrelate the data
Notice that the columns of U are a set of orthonormal vectors (norm of 1, and orthogonal to each other), so they can be regarded as basis vectors. The projection therefore corresponds to a rotation of the data in X so that the new axes are the eigenvectors. If we were to compute the covariance matrix of Xrot, we would see that it is now diagonal. A nice property of np.linalg.svd is that in its returned value U, the eigenvector columns are sorted by their eigenvalues. We can use this to reduce the dimensionality of the data by only using the top few eigenvectors, and discarding the dimensions along which the data has no variance. This is also sometimes refereed to as Principal Component Analysis (PCA) dimensionality reduction:
Xrot_reduced = np.dot(X, U[:,:100]) # Xrot_reduced becomes [N x 100]
After this operation, we would have reduced the original dataset of size [N x D] to one of size [N x 100], keeping the 100 dimensions of the data that contain the most variance. It is very often the case that you can get very good performance by training linear classifiers or neural networks on the PCA-reduced datasets, obtaining savings in both space and time.
4、whitening. The whitening operation takes the data in the eigenbasis and divides every dimension by the eigenvalue to normalize the scale. The geometric interpretation of this transformation is that if the input data is a multivariable gaussian, then the whitened data will be a gaussian with zero mean and identity covariance matrix. This step would take the form:
# whiten the data:
# divide by the eigenvalues (which are square roots of the singular values)
Xwhite = Xrot / np.sqrt(S + 1e-5)
Warning: Exaggerating noise. Note that we’re adding 1e-5 (or a small constant) to prevent division by zero. One weakness of this transformation is that it can greatly exaggerate the noise in the data, since it stretches all dimensions (including the irrelevant dimensions of tiny variance that are mostly noise) to be of equal size in the input. This can in practice be mitigated by stronger smoothing (i.e. increasing 1e-5 to be a larger number)
In practice. We mention PCA/Whitening in these notes for completeness, but these transformations are not used with Convolutional Networks. However, it is very important to zero-center the data, and it is common to see normalization of every pixel as well.
Common pitfall. An important point to make about the preprocessing is that any preprocessing statistics (e.g. the data mean) must only be computed on the training data, and then applied to the validation / test data. E.g. computing the mean and subtracting it from every image across the entire dataset and then splitting the data into train/val/test splits would be a mistake. Instead, the mean must be computed only over the training data and then subtracted equally from all splits (train/val/test).
參考鏈接：https://cs231n.github.io/neural-networks-2/#datapre