diff --git a/include/mitsuba/core/vmf.h b/include/mitsuba/core/vmf.h
index f9568c5e..3a7b23e1 100644
--- a/include/mitsuba/core/vmf.h
+++ b/include/mitsuba/core/vmf.h
@@ -76,6 +76,15 @@ public:
 	 */
 	static Float forPeakValue(Float x);
 
+	/**
+	 * \brief Estimate the vMF concentration parameter
+	 * based on the length of the mean vector that is produced
+	 * by simply averaging a set of sampled directions
+	 *
+	 * This is an unbiased estimator [Banerjee et al. 05]
+	 */
+	static Float forMeanLength(Float length);
+
 	/**
 	 * \brief Compute an appropriate concentration parameter so that
 	 * the associated vMF distribution has the mean cosine \c g.
diff --git a/src/libcore/vmf.cpp b/src/libcore/vmf.cpp
index 7d5a213b..8626fdff 100644
--- a/src/libcore/vmf.cpp
+++ b/src/libcore/vmf.cpp
@@ -127,6 +127,10 @@ static Float meanCosineFunctor(Float kappa, Float g) {
 	return VonMisesFisherDistr(kappa).getMeanCosine()-g;
 }
 
+Float VonMisesFisherDistr::forMeanLength(Float l) {
+	return (3*l - l*l*l) / (1-l*l);
+}
+
 Float VonMisesFisherDistr::forMeanCosine(Float g) {
 	if (g == 0)
 		return 0;
diff --git a/src/libpython/core.cpp b/src/libpython/core.cpp
index cbe0ff07..7d576248 100644
--- a/src/libpython/core.cpp
+++ b/src/libpython/core.cpp
@@ -512,6 +512,8 @@ static Ray transform_mul_ray(Transform *transform, const Ray &ray) { return tran
 static Transform transform_mul_transform(Transform *transform, const Transform &other) { return *transform * other; }
 
 bp::object cast(ConfigurableObject *obj) {
+	if (obj == NULL)
+		return bp::object();
 	const Class *cls = obj->getClass();
 	#define TryCast(ClassName) if (cls->derivesFrom(MTS_CLASS(ClassName))) \
 		return bp::object(ref<ClassName>(static_cast<ClassName *>(obj)))
@@ -2537,6 +2539,7 @@ void export_core() {
 		.def("getMeanCosine", &VonMisesFisherDistr::getMeanCosine)
 		.def("sample", &VonMisesFisherDistr::sample, BP_RETURN_VALUE)
 		.def("forMeanCosine", &VonMisesFisherDistr::forMeanCosine)
+		.def("forMeanLength", &VonMisesFisherDistr::forMeanLength)
 		.def("forPeakValue", &VonMisesFisherDistr::forPeakValue)
 		.def("convolve", &VonMisesFisherDistr::convolve)
 		.def("__repr__", &VonMisesFisherDistr::toString)
diff --git a/src/libpython/render.cpp b/src/libpython/render.cpp
index d78dc3a0..3f2d70d2 100644
--- a/src/libpython/render.cpp
+++ b/src/libpython/render.cpp
@@ -55,6 +55,10 @@ static Shape *shape_getShapeGroup(Shape *shape) {
 	return static_cast<Instance *>(shape)->getShapeGroup();
 }
 
+static bp::object shape_getElement(Shape *shape, int idx) {
+	return cast(shape->getElement(idx));
+}
+
 static AABB shapekdtree_getAABB(const ShapeKDTree *kdtree) {
 	return kdtree->getAABB();
 }
@@ -519,7 +523,7 @@ void export_render() {
 	BP_CLASS(Shape, ConfigurableObject, bp::no_init)
 		.def("getName", &Shape::getName, BP_RETURN_VALUE)
 		.def("isCompound", &Shape::isCompound)
-		.def("getElement", &Shape::getElement, BP_RETURN_VALUE)
+		.def("getElement", shape_getElement)
 		.def("getSurfaceArea", &Shape::getSurfaceArea)
 		.def("getAABB", &Shape::getAABB, BP_RETURN_VALUE)
 		.def("getClippedAABB", &Shape::getClippedAABB, BP_RETURN_VALUE)
diff --git a/src/sensors/orthographic.cpp b/src/sensors/orthographic.cpp
index 5b0e9e26..73247257 100644
--- a/src/sensors/orthographic.cpp
+++ b/src/sensors/orthographic.cpp
@@ -224,12 +224,12 @@ public:
 
 	Float pdfDirection(const DirectionSamplingRecord &dRec,
 			const PositionSamplingRecord &pRec) const {
-		return (pRec.measure == EDiscrete) ? 1.0f : 0.0f;
+		return (dRec.measure == EDiscrete) ? 1.0f : 0.0f;
 	}
 
 	Spectrum evalDirection(const DirectionSamplingRecord &dRec,
 			const PositionSamplingRecord &pRec) const {
-		return Spectrum((pRec.measure == EDiscrete) ? 1.0f : 0.0f);
+		return Spectrum((dRec.measure == EDiscrete) ? 1.0f : 0.0f);
 	}
 
 	Spectrum sampleDirect(DirectSamplingRecord &dRec, const Point2 &) const {