https://caffe.berkeleyvision.org/tutorial/layers/convolution.html

Caffe： Convolution Layer official document

1. Layer type Convolution

2.Input   n * c_i * h_i * w_i

3.Output n * c_o * h_o * w_o, where h_o = (h_i + 2 * pad_h - kernel_h) / stride_h + 1 and w_o likewise.

4. The Convolution layer convolves the input image with a set of learnable filters, each producing one feature map in the output image.


University of Michigan - Ann Arbor

- Python: conv_forward
- TensorFlow: tf.nn.conv2d
- Keras: Conv2D
- Pytorch: torch.nn.Conv2d
- Caffe: message ConvolutionParameter
- Theano: theano.tensor.nnet.conv.conv2d

Methods to Calculate Convolution in Python










def conv_forward(A_prev, W, b, hparameters):
    """
    Implements the forward propagation for a convolution function
    Arguments:
    A_prev -- output activations of the previous layer, numpy array of shape (m, n_H_prev, n_W_prev, n_C_prev)
    W -- Weights, numpy array of shape (f, f, n_C_prev, n_C)
    b -- Biases, numpy array of shape (1, 1, 1, n_C)
    hparameters -- python dictionary containing "stride" and "pad"
    Returns:
    Z -- conv output, numpy array of shape (m, n_H, n_W, n_C)
    cache -- cache of values needed for the conv_backward() function
    """

    ### START CODE HERE ###
    # Retrieve dimensions from A_prev's shape (≈1 line)
    (m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape

    # Retrieve dimensions from W's shape (≈1 line)
    (f, f, n_C_prev, n_C) = W.shape

    # Retrieve information from "hparameters" (≈2 lines)
    stride = hparameters['stride']
    pad = hparameters['pad']

    # Compute the dimensions of the CONV output volume using the formula given above. Hint: use int() to floor. (≈2 lines)
    n_H = int((n_H_prev - f + (2 * pad)) / stride + 1)
    n_W = int((n_W_prev - f + (2 * pad)) / stride + 1)

    # Initialize the output volume Z with zeros. (≈1 line)
    Z = np.zeros((m, n_H, n_W, n_C))

    # Create A_prev_pad by padding A_prev
    A_prev_pad = zero_pad(A_prev, pad)

    for i in range(m):  # loop over the batch of training examples
        a_prev_pad = A_prev[i]  # Select ith training example's padded activation
        for h in range(n_H):  # loop over vertical axis of the output volume
            for w in range(n_W):  # loop over horizontal axis of the output volume
                for c in range(n_C):  # loop over channels (= #filters) of the output volume

                    # Find the corners of the current "slice" (≈4 lines)
                    vert_start = stride * h
                    vert_end = stride * h + f
                    horiz_start = stride * w
                    horiz_end = stride * w + f

                    # Use the corners to define the (3D) slice of a_prev_pad (See Hint above the cell). (≈1 line)
                    a_slice_prev = A_prev_pad[i, vert_start:vert_end, horiz_start:horiz_end, :]

                    # Convolve the (3D) slice with the correct filter W and bias b, to get back one output neuron. (≈1 line)
                    Z[i, h, w, c] = conv_single_step(a_slice_prev, W[:, :, :, c], b[:, :, :, c])

    ### END CODE HERE ###

    # Making sure your output shape is correct
    assert (Z.shape == (m, n_H, n_W, n_C))

    # Save information in "cache" for the backprop
    cache = (A_prev, W, b, hparameters)

    return Z, cache

Python: conv_forward

Computes a 2-D convolution given input and 4-D filters tensors.
tf.nn.conv2d(
    input, filters, strides, padding, data_format='NHWC', dilations=None,
    name=None
)
1.input:	A Tensor. Must be one of the following types: half, bfloat16, float32, float64. A Tensor of rank at least 4. The dimension order is interpreted according to the value of data_format; with the all-but-inner-3 dimensions acting as batch dimensions. See below for details.

2.filters:	A Tensor. Must have the same type as input. A 4-D tensor of shape [filter_height, filter_width, in_channels, out_channels]

3. strides	An int or list of ints that has length 1, 2 or 4. The stride of the sliding window for each dimension of input. If a single value is given it is replicated in the H and W dimension. By default the N and C dimensions are set to 1. The dimension order is determined by the value of data_format, see below for details.

4. padding	Either the string "SAME" or "VALID" indicating the type of padding algorithm to use, or a list indicating the explicit paddings at the start and end of each dimension. When explicit padding is used and data_format is "NHWC", this should be in the form [[0, 0], [pad_top,pad_bottom], [pad_left, pad_right], [0, 0]]. When explicit padding used and data_format is "NCHW", this should be in the form [[0, 0], [0, 0],[pad_top, pad_bottom], [pad_left, pad_right]].

5. 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_shape + [height, width, channels]. Alternatively, the format could be "NCHW", the data storage order of: batch_shape + [channels, height, width].

6. dilations	An int or list of ints that has length 1, 2 or 4, defaults to 1. The dilation factor for each dimension ofinput. If a single value is given it is replicated in the H and W dimension. By default the N and C dimensions are set to 1. 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 if a 4-d tensor must be 1.

7. name	A name for the operation (optional).

TensorFlow: tf.nn.conv2d


This layer creates a convolution kernel that is convolved with the layer input to produce a tensor of outputs. If use_bias is True, a bias vector is created and added to the outputs. Finally, if activation is not None, it is applied to the outputs as well.

When using this layer as the first layer in a model, provide the keyword argument input_shape (tuple of integers, does not include the sample axis), e.g. input_shape=(128, 128, 3) for 128x128 RGB pictures in data_format="channels_last".


Keras: Conv2D class

CLASStorch.nn.Conv2d(in_channels: int, out_channels: int, kernel_size: Union[T, Tuple[T, T]], stride: Union[T, Tuple[T, T]] = 1, padding: Union[T, Tuple[T, T]] = 0, dilation: Union[T, Tuple[T, T]] = 1, groups: int = 1, bias: bool = True, padding_mode: str = 'zeros')





Pytorch: CONV2D

Caffe： Convolution Layer Sample

https://buildmedia.readthedocs.org/media/pdf/theano/latest/theano.pdf

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