Automatic and topology-preserving gradient mesh generation for image vectorization

Demonska vjera polazi od toga da se ne nalazi isključivo u nevjeri, nego je ona onkraj nevjere. Ovim radom smo prvo željeli prikazati glavne postavke najbitnijih elemenata teologalne vjere da bismo kasnije kroz filozofske teze F. Hadjadja prikazali glavna obilježja vjere zlih demona koja su duhovnog karaktera i predstavljaju veliku opasnost za čovjeka i njegovu vjeru. Unatoč različitim tumačenjima, Hadjadj želi upozoriti na to da se zli demoni ne nalaze samo među ateistima, agnosticima i ostalim pokretima koji, na neki način, niječu Božu opstojnost, nego ti zli demoni zapravo vjeruju, pa zato za polazište uzima redak iz Jakovljeve poslanice u kojoj piše da oni „vjeruju i dršću”. Na kraju smo ovim radom prikazali važnost sinteze duše i tijela, odnosno utjelovljenja u kršćanstvu jer je misterij katoličke vjere misterij utjelovljenja i nemoguće je odbacivati tjelesnost kao što je to slučaj u različitim spiritualističkim dimenzijama.Demonic faith is not strictly associated with infidelity itself, but rather exists beyond it. This work aims to present the main postulates of the most crucial elements of the theological faith in order to show, using F. Hadjadj's philosophical thesis, the main characteristics associated with evil demons, which are of the spiritual nature and present great danger for man and his faith. Despite various interpretations, Hadjadj wishes to point out that evil demons do not dwel lonly within atheists, agnostics and other movements which, in a way, negate the existence of God, but that these evil demons actually do believe, and therefore he uses as a starting point the line from the Epistle of Jacob that states that demons „believe and tremble”. In the end, this work presented the importance of the body-soul synthesis, which is the incarnation in Christianity, since the mistery of the Catholic faith is the mistery of the incarnation, and it is impossible to discard corporeality, which is the case in various spiritual dimensions

Vectorizing binary image boundaries with symmetric shape detection, bisection and optimal parameterization

Binary image boundary vectorization is the process of converting raster images into vector images represented with a sequence of Bézier curves. Two main factors in reconstructing parametric curves are to approximate the underlying structure of the boundaries as much as possible while using as few curves as possible. Existing methods do not perform well when considering both of these two main factors. In this article, we mimic the process of human vectorizing image boundaries by first segmenting the boundary points into multiple segments with the corner points. For the boundary points in each segment, we adopt the bisection method to find the largest number of points, which a single curve can fit. More curves will be added if the fitting error is larger than a predefined threshold. The process is repeated until all the points in the segment are fitted, thus minimizing the number of Bézier curves. Besides, symmetric image boundaries can be detected and used to further decrease the number of curves required. Our method can also choose the optimal parameterization method case by case to further reduce the fitting error. We make a comparison with both new and classical methods and show that our method outperforms them

Image editing and interaction tools for visual expression

Digital photography is becoming extremely common in our daily life. However, images are difficult to edit and interact with. From a user's perspective, it is important to interact freely with the images on his/her smartphone or ipad. In this thesis we develop several image editing and interaction systems with this idea in mind. We aim for creating visual models with pre-computed internal structures such that interaction is readily supported. We demonstrate that such interactable models, driven by a user's hand, can render powerful visual expressiveness, and make static pixel arrays much more fun to play with. The first system harnesses the editing power of vector graphics. We convert raster images into a vector representation using Loop's subdivision surfaces. An image is represented by a multi-resolution feature-preserving sparse control mesh, with which image editing can be done at semantic level. A user can easily put a smile on a face image, or adjust the level of scene abstractness through a simple slider. The second system allows one to insert an object from image into a new scene. The key is to correct the shading on the object such that it goes consistently with the scene. Unlike traditional approach, we use a simple shape to capture gross shading effects and a set of shading detail images to account for visual complexities. The high-frequency nature of these detail images allows a moderate range of interactive composition effects without causing alarming visual artifacts. The third system is on video clips instead of a single image. We proposed a fully automated algorithm to creat

Cartoon image vectorization based on shape subdivision

This paper presents a non-pixel-based skeletonizataon method for vectorizing cartoon images. The constrained Delaunay triangulation technique is applied to subdivide a shape into a set of non-overlapping triangles. Then, certain triangles in the triangulation are merged to remove artifacts. The skeleton of a shape is obtained from the skeletons of its constituent parts. Experiment results show that the proposed method is more accurate and efficient than a typical thinning method

Mathematical and Data-driven Pattern Representation with Applications in Image Processing, Computer Graphics, and Infinite Dimensional Dynamical Data Mining

Patterns represent the spatial or temporal regularities intrinsic to various phenomena in nature, society, art, and science. From rigid ones with well-defined generative rules to flexible ones implied by unstructured data, patterns can be assigned to a spectrum. On one extreme, patterns are completely described by algebraic systems where each individual pattern is obtained by repeatedly applying simple operations on primitive elements. On the other extreme, patterns are perceived as visual or frequency regularities without any prior knowledge of the underlying mechanisms. In this thesis, we aim at demonstrating some mathematical techniques for representing patterns traversing the aforementioned spectrum, which leads to qualitative analysis of the patterns' properties and quantitative prediction of the modeled behaviors from various perspectives. We investigate lattice patterns from material science, shape patterns from computer graphics, submanifold patterns encountered in point cloud processing, color perception patterns applied in underwater image processing, dynamic patterns from spatial-temporal data, and low-rank patterns exploited in medical image reconstruction. For different patterns and based on their dependence on structured or unstructured data, we present suitable mathematical representations using techniques ranging from group theory to deep neural networks.Ph.D