Photometric stereo for strong specular highlights

Photometric stereo (PS) is a fundamental technique in computer vision known to produce 3-D shape with high accuracy. The setting of PS is defined by using several input images of a static scene taken from one and the same camera position but under varying illumination. The vast majority of studies in this 3-D reconstruction method assume orthographic projection for the camera model. In addition, they mainly consider the Lambertian reflectance model as the way that light scatters at surfaces. So, providing reliable PS results from real world objects still remains a challenging task. We address 3-D reconstruction by PS using a more realistic set of assumptions combining for the first time the complete Blinn-Phong reflectance model and perspective projection. To this end, we will compare two different methods of incorporating the perspective projection into our model. Experiments are performed on both synthetic and real world images. Note that our real-world experiments do not benefit from laboratory conditions. The results show the high potential of our method even for complex real world applications such as medical endoscopy images which may include high amounts of specular highlights

A conservative shock filter model for the numerical approximation of conservation laws

A new shock filter model designed to sharpen numerically diffused discontinuities in a conservative fashion is presented. Besides the description of the modeling, the discussion includes a mathematically rigorous validation with respect to the meaning of the model as well as a presentation of some numerical results

A shock-capturing algorithm for the differential equations of dilation and erosion

Dilation and erosion are the fundamental operations in morphological image processing. Algorithms that exploit the formulation of these processes in terms of partial differential equations offer advantages for non-digitally scalable structuring elements and allow sub-pixel accuracy. However, the widely-used schemes from the literature suffer from significant blurring at discontinuities. We address this problem by developing a novel, flux corrected transport (FCT) type algorithm for morphological dilation / erosion with a flat disc. It uses the viscosity form of an upwind scheme in order to quantify the undesired diffusive effects. In a subsequent corrector step we compensate for these artifacts by means of a stabilised inverse diffusion process that requires a specific nonlinear multidimensional formulation. We prove a discrete maximum-minimum principle in this multidimensional framework. Our experiments show that the method gives a very sharp resolution of moving fronts, and it approximates rotation invariance very well

Highly accurate schemes for PDE-based morphology with general structuring elements

The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology