| |
| |
| ``mx.nd.Correlation`` |
| ========================================== |
| |
| Description |
| ---------------------- |
| |
| Applies correlation to inputs. |
| |
| The correlation layer performs multiplicative patch comparisons between two feature maps. |
| |
| Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels, |
| the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`. |
| |
| For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and |
| :math:`x_{2}` in the second map is then defined as: |
| |
| .. math:: |
| |
| c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o), f_{2}(x_{2} + o)> |
| |
| for a square patch of size :math:`K:=2k+1`. |
| |
| Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other |
| data. For this reason, it has no training weights. |
| |
| Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations. |
| |
| Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`, |
| by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood |
| centered around :math:`x_{1}`. |
| |
| The final output is defined by the following expression: |
| |
| .. math:: |
| |
| out[n, q, i, j] = c(x_{i, j}, x_{q}) |
| |
| where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`. |
| |
| |
| |
| |
| Arguments |
| ------------------ |
| |
| +----------------------------------------+------------------------------------------------------------+ |
| | Argument | Description | |
| +========================================+============================================================+ |
| | ``data1`` | NDArray-or-Symbol. | |
| | | | |
| | | Input data1 to the correlation. | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``data2`` | NDArray-or-Symbol. | |
| | | | |
| | | Input data2 to the correlation. | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``kernel.size`` | int (non-negative), optional, default=1. | |
| | | | |
| | | kernel size for Correlation must be an odd number | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``max.displacement`` | int (non-negative), optional, default=1. | |
| | | | |
| | | Max displacement of Correlation | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``stride1`` | int (non-negative), optional, default=1. | |
| | | | |
| | | stride1 quantize data1 globally | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``stride2`` | int (non-negative), optional, default=1. | |
| | | | |
| | | stride2 quantize data2 within the neighborhood centered | |
| | | around | |
| | | data1 | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``pad.size`` | int (non-negative), optional, default=0. | |
| | | | |
| | | pad for Correlation | |
| +----------------------------------------+------------------------------------------------------------+ |
| | ``is.multiply`` | boolean, optional, default=1. | |
| | | | |
| | | operation type is either multiplication or subduction | |
| +----------------------------------------+------------------------------------------------------------+ |
| |
| Value |
| ---------- |
| |
| ``out`` The result mx.ndarray |
| |
| |
| Link to Source Code: http://github.com/apache/incubator-mxnet/blob/1.6.0/src/operator/correlation.cc#L198 |
| |
