Photometric stereo under perspective projection

In this research, we propose a novel algorithm which recovers the surface height directly from images obtained via perspective projection. Most existing shape from shading (SFS) algorithms are developed under the assumption of an orthogonal projection model, which is a special case of the general perspective projection model. As a result, there exist substantial reconstruction errors in their real applications especially for the case when the object is not far away from the camera. By introducing an explicit triangular element surface model and combining perspective imaging geometry, we are able to relax the orthogonal projection assumption and derive a more general reflectance model with perspective projection. We formulate the perspective SFS problem as a minimization problem parameterized by surface nodal heights, and determine the surface height by solving an equivalent linear system of equations. Simulation results for several test images are given to demonstrate the performance of the proposed algorithm. The proposed perspective SFS algorithm gives more accurate results than conventional SFS algorithms and is very attractive in practical applications.

Shape from Shading (SFS) is a fundamental task in computer vision. By given information about the reflectance of an object’s surface and the position of the light source, the SFS problem is to reconstruct the 3D depth of the object from a single grayscale 2D input image. A modern class of SFS models relies on the property that the camera performs a perspective projection. The corresponding perspective SFS methods have been the subject of many investigations within the last years. The goal of this chapter is to give an overview of these developments. In our discussion, we focus on important model aspects, and we investigate some prominent algorithms appearing in the literature in more detail than it was done in previous works.

This study develops a 3D facial reconstruction system, which consists of five modules, using the orthographic projection model to approximate the perspective projection model. The first module identifies a number of feature points on the face and tracks these feature points over a sequence of facial images by the optical flow technique. The second module applies the factorization method to the orthographic model to reconstruct a 3D human face. The facial images are acquired using a pinhole camera, which are based on a perspective projection model. However, the face is reconstructed using an orthographic projection model. To compensate for the difference between these two models, the third module implements a simple and efficient method for approximating the perspective projection model. The fourth module overcomes the missing point problem, commonly arising in 3D reconstruction applications. Finally, the fifth module implements a smoothing process for the 3D surface by interpolating additional vertices.

To present two practical techniques for three-dimensional (3D) modeling of the human jaw from a sequence of intra-oral images. A data acquisition system consists of: 3D digitizing arm, CCD camera and a laser projector in addition to a software module of two 3D modeling techniques; shape from shading (SFS) and space carving (SC). Several experiments have been conducted on a sample of students at the Computer Vision and Image Processing (CVIP) Laboratory at the University of Louisville, Louisville, KY. Other experiments were performed on solid models of human jaw. The SFS technique, using perspective projection and camera calibration, extracts the 3D information from a sequence of two-dimensional images of the jaw. Data fusion of range data and 3D registration techniques develop the complete jaw model. The SC approach is implemented on a sequence of calibrated images. On the two reconstructions, we fit a mesh model to the data, in order to create a solid 3D model. The accuracy of the reconstructed 3D model of human jaw is calculated based on the measurements on real jaws. The SFS-based technique seems to provide more faithful information about the shape of the tooth tops. However, the SC algorithm successfully reconstructed 3D models of the human jaw with sub-millimeter accuracy, which is as accurate as (or even better than) the first technique without using any range measurements or laser projectors. The average error in distance calculation was found to be 0.74 mm, which is an acceptable resolution for many orthodontics and maxillofacial applications. Accurate 3D reconstruction of the human jaw enables many orthodontics and dental imaging research findings to be applied directly to a digital jaw model--not to a cast--using computer vision and medical imaging tools.

Shape-from-shading (SfS) is a fundamental problem in computer vision; it is based upon the image irradiance equation. Recently, the authors proposed to solve the image irradiance equation under the assumption of perspective projection rather than the common orthographic one. The solution was a modification of the fast marching method of Kimmel and Sethian. This paper presents an application of this novel perspective algorithm to reconstruction of medical images. We focus on gastrointestinal endoscopy and compare the two versions of the fast marching method (orthographic vs. perspective). The examples and comparison show that, unlike orthographic SfS, perspective SfS is robust and can be utilized for real-life applications.

In the areas of computer vision and computer graphics, analyzing information about three-dimensional objects from two-dimensional images is essential. Shape from shading is a very fundamental problem in computer vision, which uses features and patterns in images to infer the shape of the object in our viewing direction. The influence of solving this problem is significant. For example, a typical application of shape from shading is in astronomy, in which we can obtain landscape features of a planet by analyzing the information from the image we get.

This paper presents a new method for recovering the shape of hybrid surfaces that have both diffuse reflection and specular reflection using shape from shading (SFS). The image irradiance equation has been derived as an explicit partial differential equation (PDE) under the assumptions of orthographic camera projection and distant point light source. The reflectance model of Ward has been used to express the hybrid reflection as a linear combination from the diffuse and specular components. The resulting PDE is solved using the Lax-Friedrichs sweeping method. The proposed algorithm is evaluated by using both synthetic data and real images and the experimental results show the efficiency of the approach.

Shape-from-shading (SFS) is an important method to reconstruct three-dimensional (3D) shape of a surface in photometry and computer vision. Lambertian surface reflectance and orthographic camera projection are two fundamental assumptions which generally result in undesirable reconstructed results since inaccurate imaging model is adopted. In this paper, we propose a new fast 3D shape reconstruction approach via the SFS method relaxing the two assumptions. To this end, the Oren-Nayar reflectance and perspective projection models are used to establish an image irradiance equation which depicts the relationship between the 3D shape of non-Lambertian surfaces and its corresponding two-dimensional (2D) shading image. Considering the light attenuation of the near point source, the image irradiance equation is transformed into a static Hamilton-Jacobi partial differential equation (PDE) by solving a quadratic equation. The viscosity solution of the resultant Hamilton-Jacobi PDE is approximated by using optimal control theory and iterative fast marching method starting from a viscosity supersolution. The performance of the proposed approach is evaluated on both synthetic and real-world images and the experimental results demonstrate that the proposed approach is accurate and fast.

Shape-from-Shading (SfS) is a fundamental problem in Computer Vision. A very common assumption in this field is that image projection is orthographic. This paper re-examines the basis of SfS, the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but rather, on its natural logarithm. As such, it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then suggested; it is a modification of the Fast Marching method of Kimmel and Sethian. Following that, a comparison of the orthographic Fast Marching, perspective Fast Marching and the perspective algorithm of Prados and Faugeras on synthetic images is presented. The two perspective methods show better reconstruction results than the orthographic. The algorithm of Prados and Faugeras equates with the perspective Fast Marching. Following that, a comparison of the orthographic and perspective versions of the Fast Marching method on endoscopic images is introduced. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real-life applications in fields such as endoscopy.

The aim of this thesis is to explore computational methods for the shape from shading problem as formulated through the image irradiance equation. We seek to develop robust, efficient methods and test our algorithms on synthetic images ranging from simple smooth surfaces to complex digital terrain model data. We consider three different approaches. The first approach revisits the method of characteristic strips with a view to using more stable integration schemes than had been used in earlier works. Stable schemes coupled with projections onto the image irradiance equation are used. Although the effects of noise are thereby reduced, the solution is still deemed unsatisfactory even for very simple surfaces. The second approach considers Horn's variational technique as a basis for producing a fast solver. We devise a discretization scheme coupled with a special continuation multigrid method for this formulation. We also allow for multiple image data and explicit knowledge of the location of discontinuities in surface height and orientation. Given multiple image data, we obtain excellent results even in the presence of discontinuities. The third approach examines a class of solution techniques based on fluid flow which are new to the shape from shading literature. This formulation is ill posed in general, so we propose a regularization of the problem. We observe that the algorithm is prone to producing spurious results. Analysis shows that these are due to the non-random accumulation of errors in the computed solution. Of the three approaches considered, the variational method yields the most promising results. Efficient, good quality reconstructions are obtained, especially when data from more than one image are available.

Deep learning based computer vision approaches for smart agricultural applications

Wavelet-Based Shape from Shading

Many real objects, such as faces, sculptures, or low-reliefs are composed of many detailed parts that can not be easily modeled by an artist nor by 3D scanning. In this paper, we propose a new shape from shading (SfS) approach to rapidly model details of these objects such as wrinkles and reliefs of surfaces from one photograph. The method first determines the surface’s flat areas in the photograph. Then, it constructs a graph of relative altitudes between each of these flat areas. We circumvent the ill-posed problem of shape from shading by having the user set if some of these flat areas are a local maximum or a local minimum; additional points can be added by the user (e.g. at discontinuous creases) – this is the only user input. We use an intuitive mass-spring based minimization to determine the final position of these flat areas and a fast-marching method to generate the surface. This process can be iterated until the user is satisfied with the resulting surface. We illustrate our approach on real faces and low-relief photographs.

Shape from shading (SFS) is an important domain in computer vision. At first the paper introduces a method of shape from shading based on single image and puts forward its implementation. Then adds proper boundary conditions and adjusts the factor of brightness error function adaptively according to the results by the original algorithm, and finds accuracy of the improved algorithm by the synthesized image. At last the improved algorithm is applied to the surface height reconstruction of weld successfully, and the computing is accurate enough for the inspection on shape of weld.

This paper reports a novel method for Nucleus and Micro Nucleuses segmentation. These biological structures are very handy to biologists for relieving structural chromosome aberration. The adopted method consists into a pipeline of advanced computer vision algorithms some of them specifically tailored for the current segmentation problem. Starting from weak hypotheses on size, shape and colour of Micro Nucleuses it is possible to efficiently segment all the image features by computer vision approach. Experimental results on real images are reported