tf.nn.conv2d

tf.nn.conv2d(
    input,
    filter,
    strides,
    padding,
    use_cudnn_on_gpu=True,
    data_format='NHWC',
    dilations=[1, 1, 1, 1],
    name=None

)

Defined in tensorflow/python/ops/gen_nn_ops.py.

See the guide: Neural Network > Convolution

Computes a 2-D convolution given 4-D input and filter tensors.

Given an input tensor of shape [batch, in_height, in_width, in_channels] and a filter / kernel tensor of shape[filter_height, filter_width, in_channels, out_channels], this op performs the following:

1. Flattens the filter to a 2-D matrix with shape [filter_height * filter_width * in_channels, output_channels].
2. Extracts image patches from the input tensor to form a virtual tensor of shape [batch, out_height, out_width, filter_height * filter_width * in_channels].
3. For each patch, right-multiplies the filter matrix and the image patch vector.

In detail, with the default NHWC format,

output[b, i, j, k] =
    sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
                    filter[di, dj, q, k]

output[b, i, j, k] =
    sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
                    filter[di, dj, q, k]

output[b, i, j, k] =
    sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
                    filter[di, dj, q, k]

output[b, i, j, k] =
    sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
                    filter[di, dj, q, k]

Must have strides[0] = strides[3] = 1. For the most common case of the same horizontal and vertices strides, strides = [1, stride, stride, 1].

Args:

• input: A Tensor. Must be one of the following types: half, bfloat16, float32, float64. A 4-D tensor. The dimension order is interpreted according to the value of data_format, see below for details.
• filter: A Tensor. Must have the same type as input. A 4-D tensor of shape [filter_height, filter_width, in_channels, out_channels]
• strides: A list of ints. 1-D tensor of length 4. The stride of the sliding window for each dimension of input. The dimension order is determined by the value of data_format, see below for details.
• padding: A string from: "SAME", "VALID". The type of padding algorithm to use.
• use_cudnn_on_gpu: An optional bool. Defaults to True.
• data_format: An optional string from: "NHWC", "NCHW". Defaults to "NHWC". Specify the data format of the input and output data. With the default format "NHWC", the data is stored in the order of: [batch, height, width, channels]. Alternatively, the format could be "NCHW", the data storage order of: [batch, channels, height, width].
• dilations: An optional list of ints. Defaults to [1, 1, 1, 1]. 1-D tensor of length 4. The dilation factor for each dimension of input. If set to k > 1, there will be k-1 skipped cells between each filter element on that dimension. The dimension order is determined by the value of data_format, see above for details. Dilations in the batch and depth dimensions must be 1.
• name: A name for the operation (optional).

Returns:

A Tensor. Has the same type as input.

函数定义

tf.nn.conv2d(input, filter, strides, padding, use_cudnn_on_gpu=None, data_format=None, name=None)

功能：在给定4-D 输入和fliters的情况下，计算二维卷积。

input的shape: [batch, in_height, in_width, in_channels] 
filter的shape: [filter_height, filter_width, in_channels, out_channels]

计算过程如下： 
（１）展平filter成如下2-D matrix，其shape: [filter_height * filter_width * in_channels, output_channels] 
（２）从input tensor中提取patches构成一个virtual tensor, 其shape: [batch, out_height, out_width, filter_height * filter_width * in_channels] 
（３）对于每一个patch,　右乘上（１）中的filter matrix。即[batch, out_height, out_width, filter_height * filter_width * in_channels]　x [filter_height * filter_width * in_channels, output_channels]，其结果的shape就是[batch, out_height, out_width, output_channels]。

【注：必须有 strides[0] = strides[3] = 1】。绝大多数情况下，水平的stride和竖直的stride一样，即strides = [1, stride, stride, 1]。

输出结果的shape计算： 
‘SAME’ 类型的padding,其输出的height和width计算如下： 
out_height = ceil(float(in_height) / float(strides[1])) ceil：向上取整 
out_width = ceil(float(in_width) / float(strides[2]))

‘VALID’类型的padding, 其输出的height和width计算如下： 
out_height = ceil(float(in_height – filter_height + 1) / float(strides[1])) 
out_width = ceil(float(in_width – filter_width + 1) / float(strides[2]))

【注：tensorflow中的卷积，严格上来说是cross-correlation，而不是卷积。因为在计算的过程中，没有对filter进行翻转，而严格的卷积计算是需要对filter进行翻转的！！！】