Update documentation for correlation operation. (apache#7071)

* CorrelationOp document modified

* Fix

src/operator/correlation.cc

@@ -136,9 +136,39 @@ Operator* CorrelationProp::CreateOperator(Context ctx) const {
 }
 DMLC_REGISTER_PARAMETER(CorrelationParam);
 MXNET_REGISTER_OP_PROPERTY(Correlation, CorrelationProp)
-.describe("Applies correlation to inputs.")
 .add_argument("data1", "NDArray-or-Symbol", "Input data1 to the correlation.")
 .add_argument("data2", "NDArray-or-Symbol", "Input data2 to the correlation.")
-.add_arguments(CorrelationParam::__FIELDS__());
+.add_arguments(CorrelationParam::__FIELDS__())
+.describe(R"code(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}`.
+)code" ADD_FILELINE);
 }  // namespace op
 }  // namespace mxnet