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Gabor纹理提取•在信号处理技术领域中，Gabor变换是被公认的信号表示尤其是图像辨识的最好方法之一。•生物学领域的研究也发现，二维Gabor滤波器能够很好的描述脊椎动物大脑初级视觉皮层部分的单细胞可接收信息域的分布，两者在空频域均具有相似的局部特点，这与人类的视觉系统也是一致的。•如果从Fourier变换的角度来看，Gobor变换就是窗函数取高斯窗时的短时Fourier变换。•如果从小波变换的角度来看，Gabor变换就是小波基函数取Gabor基的小波变换。•Fourier变换是整体上将信号分解为不同的频率分量（任何信号都可分解为复正弦信号之和），Fourier变换缺乏时间的局部性信息，无法告知某些频率成分发生在哪些时间内。但是Gabor变换中的Gabor基函数包含一个高斯窗函数窗，窗的中心位置可以由我们设定（即设定时域信号取值范围），所以某个信号经过Gabor变换后在Gabor频域的表现与信号时域表现就可以联系起来了。Gabor纹理•1、Gabor滤波•构建gabor滤波器组，多方向多尺度对图像进行gabor滤波。•2、纹理提取•对每个方向每个尺度的滤波图像进行纹理特征描述Gabor滤波•指定方向，自动尺度•指定方向，指定尺度纹理提取方法•usingthemagnituderesponse幅度响应•applyingspatialsmoothing空间平滑•usingonlytherealcomponent实部分量•usinganon-linearsigmoidalfunction非线性S型函数•usingpixeladjacencyinformation像素邻接信息•applyingfullwaverectification全波整流•creatingmomentsbasedonthespatial-frequencyplane空间频率平面•TextureSegmentationUsingGaborFilters•KhaledHammoudaProf.EdJernigan•UniversityofWaterloo,Ontario,Canada•滑铁卢大学Naotoshi@马里兰大学•构建滤波器组（自动尺度）•用滤波器对图像进行卷积•提取纹理Gabor滤波器组参数•λ：波长的余弦因子（Lambda）•θ：方向角度（Theta）•ψ：相位偏移角度（Psi）•σ：isthestandarddeviationoftheGaussiandeterminesthe(linear)sizeofthereceptivefield尺寸（Sigma）•ϒ：空间的长宽比（Gamma）•b：半响应的空间频率带宽滤波参数选择•ϒ=1•b=1•ψ=0时对应的是gabor的实部•θ:0,30,60,90,120,150•λ=1/fi=1,2,...,log2(Nc/8)Nc图像的宽，2的幂次方0FL(i)0.250.25=FH(i)0.5.滤波器纹理提取•Gabor滤波器组对图像卷积•S型（非线性）函数•高斯滤波•Jain在论文中提到了平均绝对偏差averageabsolutedeviation(AAD)1、非线性转换•S函数公式•归一化α为常数=0.25（论文中）2、高斯滤波•这里的σ为前面滤波器组中σ的3倍。（Sigma）B.S.ManjunathandW.Y.Ma@加州大学圣塔芭芭拉分校•构建滤波器组•滤波器作为基函数，对图像进行傅里叶变换•提取纹理一、Gabor滤波器组__其中x=xcosθ+ysinθ,y=--xsinθ+ycosθσx和σy是缩放比例常数，控制高斯函数在x轴和y轴的伸缩程度，它们决定了一象素点周围参与加权和的有效范围，θ是滤波器的方向参数，w是正弦曲线的径向频率，决定了滤波器在频域中的位置。•1式为gabor函数，1式是其对应的傅里叶形式•σu=1/2πσx,andσv,=1/2πσy•Ul和Uh是感兴趣的最低频和最高频•θ=nπ/K，k是方向个数•m=0,1,...,S–1，S是尺度个数纹理提取•原图傅里叶变换•Gabor基傅里叶•相乘•反变换•求均值方差其他人的做法•构建滤波器组，指定方向和尺度•滤波器对图像进行卷积•提取纹理11.1782,-0.3842114.32678,-0.1873254.06591,-1.257519.0114,-0.3959566.48956,-0.3882636.76781,-96.874123.57,-0.6552979.25225,-0.54753113.5566,-0.63187615.2156,-0.2008755.91,-0.5329514.46158,-102.87413.8364,-0.2637444.34812,-0.3436289.96749,-0.47539220.7942,-0.2248974.17269,-0.24896413.7891,-2.2801511.5148,-0.3045316.32335,-0.3829235.00933,-0.051069113.9723,-0.2362146.95537,-0.2755568.10471,-0.24663214.8846,-0.089657311.9098,-0.08079938.82971,-0.16581814.622,-0.8208338.52627,-0.4228233.77919,-0.52287613.032,-0.4014087.14051,-0.44417113.508,-0.4493819.89683,-0.3095415.15573,-0.14304714.7604,-0.3983713.312,-0.3880057.30762,-0.23384.83414,-0.15917617.626,-0.1399728.32798,-0.4033311.3599,-0.12185816.7661,-0.5475914.7426,-0.87751313.4699,-0.12144310.7712,-0.277789.46838,-0.3563355.39981,-0.214498.05304,-0.0919698.38209,-0.44715517.9332,-0.6784639.30488,-0.4152766.79565,-0.33681717.9486,-0.2285889.90672,-0.12658510.4479,-0.19331710.5295,-0.072123815.2226,-0.13939310.9331,-0.2253224.6918,-0.22250915.9819,-0.32528913.9776,-0.14312221.6695,-0.1010279.89434,-0.42090114.3628,-0.05339098.58233,-0.1775197.88405,-0.15565311.662,-0.047579930.5137,-0.2467648.89936,-0.30493410.233,-0.3625535.6045,-0.1422911.6135,-0.44786615.5013,-0.08693689.81986,-0.016363618.6464,-0.065864716.2147,-0.22056841.0453,-0.11678119.8301,-0.17400319.5187,-0.21069439.423,-0.1141089.83007,-0.30298921.5331,-0.38082414.476,-0.07096098.63773,-0.12058816.1545,-0.13262842.6591,-0.17957110.6891,-0.24125814.2059,-0.32642843.7337,-0.16428316.7868,-0.14845420.3156,-0.25589711.7229,-0.066549823.7271,-0.23856926.2916,-0.38964145.992,-0.15740225.291,-0.11423831.3131,-0.1026979.0196,-0.037760613.322,-0.080965921.7491,-0.30889723.9904,-0.039876413.0261,-0.2251718.8524,-0.13705564.3372,-0.11845212.9064,-0.1562721.6449,-0.13215557.4063,-0.0555283