code: def spatial_kernel_embedding(
      kernel_type: str, grids: Dict[str, Tensor]
  ) -> Tensor:
      r"""Compute embeddings for cartesian and polar parametrizations."""
      factors = {
          "phi": 1.0,
          "rho": pi / sqrt2,
          "x": pi / 2,
          "y": pi / 2,
      }
      if kernel_type == "cart":
          coeffs_ = "xy"
          params_ = ["x", "y"]
      elif kernel_type == "polar":
          coeffs_ = "rhophi"
          params_ = ["phi", "rho"]
  
      # Infer patch_size.
      keys = list(grids.keys())
      patch_size = grids[keys[0]].shape[-1]
  
      # Scale appropriately.
      grids_normed = {k: v * factors[k] for k, v in grids.items()}
      grids_normed = {
          k: v.unsqueeze(0).unsqueeze(0).float()
          for k, v in grids_normed.items()
      }
  
      # x,y/rho,phi kernels.
      vm_a = VonMisesKernel(
          patch_size=patch_size, coeffs=COEFFS[coeffs_]
      )
      vm_b = VonMisesKernel(
          patch_size=patch_size, coeffs=COEFFS[coeffs_]
      )
  
      emb_a = vm_a(grids_normed[params_[0]]).squeeze()
      emb_b = vm_b(grids_normed[params_[1]]).squeeze()
  
      # Final precomputed position embedding.
      kron_order = get_kron_order(vm_a.d, vm_b.d)
      spatial_kernel = emb_a.index_select(
          0, kron_order[:, 0]
      ) * emb_b.index_select(0, kron_order[:, 1])
      return spatial_kernel
  
imports: from typing import Any, Dict, List, Tuple, Union
  import torch
  import torch.nn.functional
  from torch import nn
  from kornia.constants import pi
  from kornia.core import Tensor, cos, sin, tensor, zeros
  from kornia.filters import GaussianBlur2d, SpatialGradient
  from kornia.geometry.conversions import cart2pol
  from kornia.utils import create_meshgrid
  from kornia.utils.helpers import map_location_to_cpu
label_desc: Use image node_id 3 for calling a global function with example usage: spatial_kernel_embedding(kernel_type, grids) and returns: spatial_kernel