[core] Fix flow field Jacobian determinant calculation

Author: aschuh-hf

src/deepali/core/flow.py

@@ -146,7 +146,8 @@ def divergence(
     kwargs = dict(mode=mode, sigma=sigma, spacing=spacing, stride=stride)
     which = FlowDerivativeKeys.divergence(spatial_dims=D)
     deriv = flow_derivatives(flow, which=which, **kwargs)
-    div = torch.zeros((N, 1) + flow.shape[2:], dtype=flow.dtype, device=flow.device)
+    ref = deriv["du/dx"]
+    div = torch.zeros((N, 1) + ref.shape[2:], dtype=ref.dtype, device=ref.device)
     for value in deriv.values():
         div = div.add_(value)
     return div
@@ -378,22 +379,44 @@ def jacobian_det(
     kwargs = dict(mode=mode, sigma=sigma, spacing=spacing, stride=stride)
     which = FlowDerivativeKeys.jacobian(spatial_dims=D)
     deriv = flow_derivatives(flow, which=which, **kwargs)
-    jac: Optional[Tensor] = None
-    for perm in permutations(range(D)):
-        term: Optional[Tensor] = None
-        for i, j in zip(range(D), perm):
-            dij = deriv[FlowDerivativeKeys.symbol(i, j)]
-            if i == j:
-                dij = dij.add_(1)  # T(x) = x + u(x)
-            term = dij if term is None else term.mul_(dij)
-        assert term is not None
-        if jac is None:
-            jac = term
-        elif is_even_permutation(perm):
-            jac = jac.add_(term)
-        else:
-            jac = jac.sub_(term)
-    assert jac is not None
+    # Add 1 to diagonal elements of Jacobian matrix, because T(x) = x + u(x)
+    for i in range(D):
+        deriv[FlowDerivativeKeys.symbol(i, i)].add_(1)
+    if D == 2:
+        a = deriv["du/dx"]
+        b = deriv["du/dy"]
+        c = deriv["dv/dx"]
+        d = deriv["dv/dy"]
+        jac = a.mul(d).sub_(b.mul(c))
+    elif D == 3:
+        a = deriv["du/dx"]
+        b = deriv["du/dy"]
+        c = deriv["du/dz"]
+        d = deriv["dv/dx"]
+        e = deriv["dv/dy"]
+        f = deriv["dv/dz"]
+        g = deriv["dw/dx"]
+        h = deriv["dw/dy"]
+        i = deriv["dw/dz"]
+        term_1 = a.mul(e.mul(i).sub_(f.mul(h)))
+        term_2 = b.mul(d.mul(i).sub_(g.mul(f)))
+        term_3 = c.mul(d.mul(h).sub_(e.mul(g)))
+        jac = term_1.sub(term_2).add(term_3)
+    else:
+        jac: Optional[Tensor] = None
+        for perm in permutations(range(D)):
+            term: Optional[Tensor] = None
+            for i, j in zip(range(D), perm):
+                dij = deriv[FlowDerivativeKeys.symbol(i, j)]
+                term = dij if term is None else term.mul_(dij)
+            assert term is not None
+            if jac is None:
+                jac = term
+            elif is_even_permutation(perm):
+                jac = jac.add_(term)
+            else:
+                jac = jac.sub_(term)
+        assert jac is not None
     return jac