前段時間在standford university的計算機視覺：演算法與應用這門課上做了一個小作業——利用詞袋實現場景識別（Scene recognition with bag of words），下面整理如下：

一、詞袋模型

         最先是由Josef等基於自然語言處理模型而提出的。這一模型在文件分類裡廣為應用，通過統計each word的frequency來作為分類器的特徵。類比一篇文章由很多文字(textual words) 組合而成，如果將一張圖片表示成由許多 視覺單詞（visual words）組合而成，就能將過去在文字檢索（text retrieval

          下面通過一個簡單的例子來說明詞袋在文字處理中的應用：

           如下兩篇簡單的文件;

        基於這兩篇文件建立一個字典（Dictionary）如下：

        易見這個字典由10個distinct word構成，將其作為indexes，我們可將兩篇文件表示為如下的10-entry vector：

通俗的講：

Bag-of-words model實際就是把文件表示成向量,其中vector的維數就是字典所含詞的個數，在上例中，vector中的第i個元素就是統計該文件中對應（字典）dictionry中的第i個單詞出現的個數，因此可認為BoW model就是統計詞頻直方圖的簡單文件表示方法。

 二、 詞袋模型在計算機視覺中的應用

類別識別的最簡單的演算法之一是詞袋（bag of words，也稱為特徵袋，即bag of features或“關鍵點袋”bag of keypoints）方法。詞袋類別識別系統的典型處理框架如下圖所示：

    二、安裝
    1. 將所下載的二進位制包解壓縮到某個位置，如D:\盤

    2.將解壓完後的vlfeat檔案複製到matlab安裝目錄toolbox資料夾下
    3. 開啟matlab，輸入edit startup.m建立啟動檔案startup.m
    4. 在startup.m中編輯發下內容（注意，如果將vlfeat安裝在不同的地方，需要將以下的”D:\”改為你所安裝的地址）：

function image_feats = get_tiny_images(image_paths)
% image_paths is an N x 1 cell array of strings where each string is an
%  image path on the file system.
% image_feats is an N x d matrix of resized and then vectorized tiny
%  images. E.g. if the images are resized to 16x16, d would equal 256.
% small square resolution, e.g. 16x16. You can either resize the images to
% square while ignoring their aspect ratio or you can crop the center
% square portion out of each image. Making the tiny images zero mean and
% unit length (normalizing them) will increase performance modestly.
%file_paths = cell(System.IO.Directory.GetDirectories('D:\MATLAB\R2014a\bin\data3'));
%celldisp(file_paths);
[m,n] = size(image_paths);
d = 256;
%image_feats = [];
image_feats = zeros(m,d);
for i = 1:m
    %string = image_paths{i};
    s = num2str(cell2mat(image_paths(i)));
    image = imread(s);
    image = imresize(image,[16,16]);
    image = reshape(image,1,256);
    %image = image/norm(image);   %normalize the tiny image
    image = image - mean(image);  %make the tiny image zero mean
    image_feats(i,1:d) = image;
    %image_feats = [image_feats;image];
end

function predicted_categories = nearest_neighbor_classify(train_image_feats, train_labels, test_image_feats)
% image_feats is an N x d matrix, where d is the dimensionality of the
%  feature representation.
% train_labels is an N x 1 cell array, where each entry is a string
%  indicating the ground truth category for each training image.
% test_image_feats is an M x d matrix, where d is the dimensionality of the
%  feature representation. You can assume M = N unless you've modified the
 D = vl_alldist2(X,Y) 
    http://www.vlfeat.org/matlab/vl_alldist2.html
    returns the pairwise distance matrix D of the columns of X and Y. 
    D(i,j) = sum (X(:,i) - Y(:,j)).^2
    Note that vl_feat represents points as columns vs this code (and Matlab
    in general) represents points as rows. So you probably want to use the
    transpose operator ' 
   vl_alldist2 supports different distance metrics which can influence
   performance significantly. The default distance, L2, is fine for images.
   CHI2 tends to work well for histograms.
 
  [Y,I] = MIN(X) if you're only doing 1 nearest neighbor, or
  [Y,I] = SORT(X) if you're going to be reasoning about many nearest
  neighbors 

%}
[N,d] = size(test_image_feats);
predicted_categories = cell(N,1);
dist = zeros(N,N);
for i = 1:N
    for j = 1:N
        dist(i,j) = vl_alldist2(test_image_feats(i,:)',train_image_feats(j,:)');
    end
    [Y,I] = min(dist(i,:));
    predicted_categories(i,1) = train_labels(I);
end

function vocab = build_vocabulary( image_paths, vocab_size )
% The inputs are images, a N x 1 cell array of image paths and the size of 
% the vocabulary.
[centers, assignments] = vl_kmeans(X, K)
 http://www.vlfeat.org/matlab/vl_kmeans.html
  X is a d x M matrix of sampled SIFT features, where M is the number of
   features sampled. M should be pretty large! Make sure matrix is of type
   single to be safe. E.g. single(matrix).
  K is the number of clusters desired (vocab_size)
  centers is a d x K matrix of cluster centroids. This is your vocabulary.
N = size(image_paths,1);
image_sampledSIFT = [];
for i = 1:4:N
    s = num2str(image_paths(i));    %%s = num2str(cell2mat(image_paths(i)));
    img = single(imread(s));
    [locations,SIFT_features] = vl_dsift(img,'STEP',10);
    SIFT_features = single(SIFT_features);
    image_sampledSIFT = [image_sampledSIFT SIFT_features];
end
[vocab assignments] = vl_kmeans(image_sampledSIFT,vocab_size);

function image_feats = get_bags_of_sifts(image_paths)
% image_paths is an N x 1 cell array of strings where each string is an
% image path on the file system.
%{Useful functions:
[locations, SIFT_features] = vl_dsift(img) 
 http://www.vlfeat.org/matlab/vl_dsift.html
 locations is a 2 x n list list of locations, which can be used for extra
  credit if you are constructing a "spatial pyramid".
 SIFT_features is a 128 x N matrix of SIFT features
D = vl_alldist2(X,Y) 
   http://www.vlfeat.org/matlab/vl_alldist2.html
    returns the pairwise distance matrix D of the columns of X and Y. 
    D(i,j) = sum (X(:,i) - Y(:,j)).^2  %}

</pre><pre name="code" class="html" style="color: rgb(51, 51, 51);">

load('vocab.mat')
fprintf('vocab loaded\n')
vocab_size = size(vocab, 2);
image_feats = [];
for i = 1:size(image_paths)
    img = single(imread(num2str(cell2mat(image_paths(i)))));
    [locations,SIFT_features] = vl_dsift(img,'STEP',10);
    SIFT_features = single(SIFT_features);
    D = vl_alldist2(vocab,SIFT_features);
    [X,I] = min(D);
    histogram = zeros(vocab_size,1);
    for j = 1:vocab_size
        histogram(I(j)) = histogram(I(j)) + 1;
    end
    histogram = histogram/norm(histogram);
    image_feats(i,:) = histogram';
end

同樣也是利用最近鄰分類進行分類。

結果如下：