A Precision Analysis of Camera Distortion Models.

This paper addresses the question of identifying the right camera direct or inverse distortion model, permitting a high subpixel precision to fit to real camera distortion. Five classic camera distortion models are reviewed and their precision is compared for direct or inverse distortion. By definition, the three radially symmetric models can only model a distortion radially symmetric around some distortion center. They can be extended to deal with non-radially symmetric distortions by adding tangential distortion components, but still may be too simple for very accurate modeling of real cameras. The polynomial and the rational models instead miss a physical or optical interpretation, but can cope equally with radially and non-radially symmetric distortions. Indeed, they do not require the evaluation of a distortion center. When requiring high precisions, we found that the distortion modeling must also be evaluated primarily as a numerical problem. Indeed, all models except the polynomial involve a non-linear minimization, which increases the numerical risk. The estimation of a polynomial distortion model leads instead to a linear problem, which is secure and much faster. We concluded by extensive numerical experiments that, although high degree polynomials were required to reach a high precision of 1/100 pixels, such polynomials were easily estimated and produced a precise distortion modeling without overfitting. Our conclusion is validated by three independent experimental setups: the models were compared first on the lens distortion database of the Lensfun library by their distortion simulation and inversion power; second by fitting real camera distortions estimated by a non parametric algorithm; and finally by the absolute correction measurement provided by the photographs of tightly stretched strings, warranting a high straightness.

Tree-based Morse regions: a topological approach to local feature detection.

This paper introduces a topological approach to local invariant feature detection motivated by Morse theory. We use the critical points of the graph of the intensity image, revealing directly the topology information as initial interest points. Critical points are selected from what we call a tree-based shape-space. In particular, they are selected from both the connected components of the upper level sets of the image (the Max-tree) and those of the lower level sets (the Min-tree). They correspond to specific nodes on those two trees: 1) to the leaves (extrema) and 2) to the nodes having bifurcation (saddle points). We then associate to each critical point the largest region that contains it and is topologically equivalent in its tree. We call such largest regions the tree-based Morse regions (TBMRs). The TBMR can be seen as a variant of maximally stable extremal region (MSER), which are contrasted regions. Contrarily to MSER, TBMR relies only on topological information and thus fully inherit the invariance properties of the space of shapes (e.g., invariance to affine contrast changes and covariance to continuous transformations). In particular, TBMR extracts the regions independently of the contrast, which makes it truly contrast invariant. Furthermore, it is quasi-parameter free. TBMR extraction is fast, having the same complexity as MSER. Experimentally, TBMR achieves a repeatability on par with state-of-the-art methods, but obtains a significantly higher number of features. Both the accuracy and robustness of TBMR are demonstrated by applications to image registration and 3D reconstruction.

High-precision camera distortion measurements with a "calibration harp".

This paper addresses the high-precision measurement of the distortion of a digital camera from photographs. Traditionally, this distortion is measured from photographs of a flat pattern that contains aligned elements. Nevertheless, it is nearly impossible to fabricate a very flat pattern and to validate its flatness. This fact limits the attainable measurable precisions. In contrast, it is much easier to obtain physically very precise straight lines by tightly stretching good quality strings on a frame. Taking literally "plumb-line methods," we built a "calibration harp" instead of the classic flat patterns to obtain a high-precision measurement tool, demonstrably reaching 2/100 pixel precisions. The harp is complemented with the algorithms computing automatically from harp photographs two different and complementary lens distortion measurements. The precision of the method is evaluated on images corrected by state-of-the-art distortion correction algorithms, and by popular software. Three applications are shown: first an objective and reliable measurement of the result of any distortion correction. Second, the harp permits us to control state-of-the art global camera calibration algorithms: it permits us to select the right distortion model, thus avoiding internal compensation errors inherent to these methods. Third, the method replaces manual procedures in other distortion correction methods, makes them fully automatic, and increases their reliability and precision.