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SPD matrix distances and their properties

Distance	Formula	Geodesic	Affine invariance	Scale invariance	Rotation invariance	Inversion invariance
Frobenius	$\beta$	No	No	No	Yes	No
Log-Frobenius		Yes	Yes	Yes	Yes	Yes
Affine invariant		Yes	No	Yes	Yes	Yes

$\beta$

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Kalman filter

SPD matrices

• Tyagi, A. and Davis, J. W. (2008). “A Recursive Filter For Linear Systems on Rieman- nian Manifolds.” In IEEE Conference on Computer Vision and Pattern Recognition.

Grassmannians

• Srivastava, A. and Klassen, E. (2004). “Bayesian and Geometric Subspace Tracking.” Advances in Applied Probability, 36(1): 43–56.

Stiefel manifold

• Tompkins, F. and Wolfe, P. J. (2007). “Bayesian Filtering on the Stiefel Manifold.” In Computational Advances in Multi-Sensor Adaptive Processing, 261 – 264.

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Simulators

3D content creation

• Blender

Summary | Examples

Indoor

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UnrealCV

Simulator for Computer Vision based on Unreal Engine 4. Main docs.

Installation

Compiled binaries for Windows, Linux and MacOS available. Binaries are containing UnrealCV along with one of five prepackaged scenes (4 indoor, 1 outdoor).

RealisticRendering scene is also available via Docker:

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import bpy
import json
import os


class DataCombiner(object):

    def __init__(self, path_to_renders, path_to_groundtruth):
        self.path_to_groundtruth = path_to_groundtruth
        bpy.data.scenes['Scene'].render.filepath = path_to_renders