第一:内核大小

2D卷积的内核大小如下

First: The Kernel size

The kernel size for 2D convolution is as follows

[ height, width, input_filters, output_filters ]

第三维尺寸与输入过滤器的尺寸相同.这很关键.

The third dimension is of the same size as the input filters. This is critical.

让我们考虑一下如何手动进行卷积.步骤如下:

Let's consider how convolution is done manually. Here are the steps:

• 从一批图像(BatchSize，height，width，filters)中获取补丁
• 将其重塑为[BatchSize，高度*宽度*过滤器]
• 矩阵将其乘以整形后的内核[高度*宽度*过滤器，输出过滤器]
• 这时我们的数据是[BatchSize，output_filters]形状
• 通过在整个批次中广播来增加形状[output_filters]的偏差

输出是每个补丁的过滤器.

The output is the filters for each patch.

鉴于我们知道卷积中的权重是整形的像 [高度，宽度，input_filters，output_filters] ，我们想正确地应用 [高度，宽度] 的蒙版，可以像这样广播该蒙版

Given that we know the weights in the convolution are shaped like [ height, width, input_filters, output_filters ] and we want to properly apply a mask of [ height, width ], can can just broadcast that mask like so

masked_weight = weight * mask.reshape([height,width,1,1])

我们的Tensorflow keras层可以这样写

Our Tensorflow keras layer could be written like so

class MaskedConv2D(tf.keras.layers.Layer):
    def __init__(self, *args, **kwargs):
        super(MaskedConv2D, self).__init__()
        self.conv2d = tf.keras.layers.Conv2D(*args, **kwargs)
        
    def build(self, input_shape):
        self.conv2d.build(input_shape[0])
        self._convolution_op = self.conv2d._convolution_op
        
    def masked_convolution_op(self, filters, kernel, mask):
        return self._convolution_op(filters, tf.math.multiply(kernel, tf.reshape(mask, mask.shape + [1,1] )))
        
    def call(self, inputs):
        x, mask = inputs
        self.conv2d._convolution_op = functools.partial(self.masked_convolution_op, mask=mask)
        return self.conv2d.call(x)

我们可以使用以下脚本对其进行测试

and we can test it with the following script

mcon = MaskedConv2D(filters=2,kernel_size=[3,3])

# hack: initialize it by running some data through it
mcon((np.ones([1,4,4,3], dtype=np.float32), tf.constant([[1,1,0],[1,1,1],[0,1,1]], dtype=tf.float32)))

# set all the weights to 1 for testing
mcon.set_weights([ np.ones([3,3,3,2]) , np.zeros([2]) ])

# pass in a matrix of 1s and mask out 2 elements for each input filter
mcon((np.ones([1,4,4,3], dtype=np.float32), tf.constant([[1,1,0],[1,1,1],[0,1,1]], dtype=tf.float32)))

具有可预测的输出

<tf.Tensor: shape=(1, 2, 2, 2), dtype=float32, numpy=
    array([[[[21., 21.],
             [21., 21.]],
            [[21., 21.],
             [21., 21.]]]], dtype=float32)>