# 1.6 三维卷积（Convolutions over volumes）

3通道的RGB图片对应的滤波器算子也是3通道的。例如一个图片是6 x 6 x 3，分别表示图片的高度（height）、宽度（weight）和通道（#channel）

3通道图片的卷积运算与单通道图片的卷积运算基本一致。过程是将每个单通道（R，G，B）与对应的filter进行卷积运算求和，然后再将3通道的和相加，得到输出图片的一个像素值

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/9b0b0e9062f8814a6a462ea64449f89e.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/9b0b0e9062f8814a6a462ea64449f89e.png)

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/2fd0c97947a3e8222e78d550a317366d.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/2fd0c97947a3e8222e78d550a317366d.png)

不同通道的滤波算子可以不相同。例如R通道filter实现垂直边缘检测，G和B通道不进行边缘检测，全部置零，或者将R，G，B三通道filter全部设置为水平边缘检测

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/d088cafb50cabd6837d95c03c953e920.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/d088cafb50cabd6837d95c03c953e920.png)

为了进行多个卷积运算，实现更多边缘检测，可以增加更多的滤波器组。例如设置第一个滤波器组实现垂直边缘检测，第二个滤波器组实现水平边缘检测。做完卷积，然后把这两个4×4的输出堆叠在一起，第一个放到前面，第二个放到后面，就得到一个4×4×2的输出立方体

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/794b25829ae809f93ac69f81eee79cd1.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/794b25829ae809f93ac69f81eee79cd1.png)

不同滤波器组卷积得到不同的输出，个数由滤波器组决定

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/d590398749e3f5f3ac230ab25116c4b7.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/d590398749e3f5f3ac230ab25116c4b7.png)

若输入图片的尺寸为n x n x$$n\_c$$，filter尺寸为f x f x $$n\_c$$，则卷积后的图片尺寸为(n-f+1) x (n-f+1) x $${n}'\_c$$(默认padding为1）。$$n\_c$$为图片通道数目，$${n}'\_c$$为滤波器组个数


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