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%高斯背景建模（）
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clear?all
tic;%計時開始%取第一幅符合要求的背景圖、
%?------------??frame?size?variables?幀的變量定義-----------------------

fr?=?imread（‘00.jpg‘）;???????????%?讀取第一幀圖片作為背景
fr_bw?=?rgb2gray（fr）;?????%?將背景轉(zhuǎn)換為灰度圖像
fr_size?=?size（fr）;??????%取幀的大小???????
width?=?fr_size（2）;??????%將第一幀圖片矩陣列數(shù)賦給width
height?=?fr_size（1）;??????%第一幀圖片矩陣行數(shù)賦給height
fg?=?zeros（height?width）;??%定義一個相同大小的零矩陣?前景
bg_bw?=?zeros（height?width）;%背景

%?------------?mog?variables?混合高斯模型變量定義----------------------------------

C?=?3;??????????????????????????????????%?組成混合高斯單高斯數(shù)目（一般為3~5）
M?=?3;??????????????????????????????????%?組成背景的數(shù)目
D?=?2.5;????????????????????????????????%?閾值（一般為2.5倍的標(biāo)準(zhǔn)差）
alpha?=?0.01;???????????????????????????%?學(xué)習(xí)率?（在?0?到?1之間）?（from?paper?0.01）決定更新速度
thresh?=?0.25;??????????????????????????%?前景閾值?（0.25?or?0.75?in?paper）
sd_init?=?6;????????????????????????????%?初始化標(biāo)準(zhǔn)差?（for?new?components）?var?=?36?in?paper
w?=?zeros（heightwidthC）;??????????????%?初始化權(quán)值數(shù)組矩陣
mean?=?zeros（heightwidthC）;???????????%?像素均值矩陣
sd?=?zeros（heightwidthC）;?????????????%?像素標(biāo)準(zhǔn)差矩陣
u_diff?=?zeros（heightwidthC）;?????????%?與均值作差的矩陣
p?=?alpha/（1/C）;????????????????????????%?參與學(xué)習(xí)率?（用于更新?mean?和?sd）
rank?=?zeros（1C）;??????????????????????%?梯度組成部分，越大愈好?（w/sd）


%?----?initialize?component?means?and?weights?初始化均值和權(quán)值-----------

pixel_depth?=?8;????????????????????????%?像素深度為8位
pixel_range?=?2^pixel_depth?-1;?????????%?像素范圍2的7次方0-255

for?i=1:height
????for?j=1:width
????????for?k=1:C
????????????
????????????mean（ijk）?=?rand*pixel_range;?????%?隨機(jī)數(shù)?（0-255）
????????????w（ijk）?=?1/C;?????????????????????%?權(quán)值數(shù)組矩陣均勻
????????????sd（ijk）?=?sd_init;????????????????%?初始化?sd_init
????????????
????????end
????end
end

%------------?process?frames?處理幀-----------------------------------

for?n?=?0001:0200???????%循環(huán)共有200幅圖片

????fr?=?imread（[‘0‘int2str（n）‘.jpg‘]）;??????%?讀取幀
????fr_bw?=?rgb2gray（fr）;???????%?轉(zhuǎn)換為灰度圖像
????
????%?calculate?difference?of?pixel?values?from?mean計算像素差值
????for?m=1:C
????????u_diff（::m）?=?abs（double（fr_bw）?-?double（mean（::m）））;
????end
?????
????%?update?gaussian?components?for?each?pixel?更新每個像素的背景模型
????for?i=1:height
????????for?j=1:width
????????????
????????????match?=?0;
????????????for?k=1:C???????????????????????
????????????????if?（abs（u_diff（ijk））?<=?D*sd（ijk））???????%?像素匹配了模型
????????????????????
????????????????????match?=?1;??????????????????????????%?設(shè)置匹配記號
????????????????????
????????????????????%?update?weights?mean?sd?p?
????????????????????%?更新???權(quán)值?????均值??標(biāo)準(zhǔn)差??參數(shù)學(xué)習(xí)率
????????????????????w（ijk）?=?（1-alpha）*w（ijk）?+?alpha;
????????????????????p?=?alpha/w（ijk）;??????????????????
????????????????????mean（ijk）?=?（1-p）*mean（ijk）?+?p*double（fr_bw（ij））;
????????????????????sd（ijk）?=???sqrt（（1-p）*（sd（ijk）^2）?+?p*（（double（fr_bw（ij））?-?mean（ijk）））^2）;
????????????????else??????