Generalized Diffusion Curves: An Improved Vector Representation for Smooth‐Shaded Images

Jeschke, Stefan

doi:10.1111/cgf.12812

Cited by 14 publications

(25 citation statements)

References 25 publications

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“…In addition to reconstruction results of the raster images, our method also makes it easy to perform high object-level editing operations. Most of the diffusion curves methods edit each curve separately rather than an object [9,17,35]. The image vectorization method proposed by [32] which also show another three examples of depth-aware segmentation and object-based diffusion curves image editing.…”

Section: Resultsmentioning

confidence: 99%

“…Sun et al [28] proposed a fast multipole representation for diffusion curve images by introducing a new vector graphics primitive called diffusion points; their technique can render millions of diffusion curves in real time. Jeschke [9] introduced a generalized and improved diffusion curve representation based on a spatial blending of multiple Laplace functions and a new edge blur formulation. However, these diffusion curves are defined manually by users, not extracted automatically from an image, making the technique unsuitable for vectorization of detailed real-world images.…”

Section: Related Workmentioning

confidence: 99%

“…Unlike mesh-based [12] and patch-based [31] vector graphics representations, a DCI consists of a sparse set of disconnected paths, making it difficult to extract and manipulate the subset of paths that contribute to an object in the image. Current techniques are typically limited to curve-level editing [9,11,17].…”

Section: Introductionmentioning

confidence: 99%

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Depth-aware image vectorization and editing

Jiang

Ding

et al. 2019

Vis Comput

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Image vectorization is one of the primary means of creating vector graphics. The quality of a vectorized image depends crucially on extracting accurate features from input raster images. However, correct object edges can be difficult to detect when color gradients are weak. We present an image vectorization technique that operates on a color image augmented with a depth map and uses both color and depth edges to define vectorized paths. We output a vectorized result as a diffusion curve image. The information extracted from the depth map allows us more flexibility in the manipulation of the diffusion curves, in particular permitting high-level object segmentation. Our experimental results demonstrate that this method achieves high reconstruction quality and provides greater control in the organization and editing of vectorized images than existing work based on diffusion curves.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Depth-aware image vectorization and editing

Jiang

Ding

et al. 2019

Vis Comput

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“…Ostromoukhov and Hersch [OH99] used a multi‐colour dithering approach to generate colour images made of artistic shapes. Many approaches convert a raster image into vector graphics, such as work done by Jeschke [Jes16], who introduced a generalized formulation for diffusion curve images. Durand et al .…”

Section: Related Workmentioning

confidence: 99%

LinesLab: A Flexible Low‐Cost Approach for the Generation of Physical Monochrome Art

Stoppel

Brückner

2019

Computer Graphics Forum

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The desire for the physical generation of computer art has seen a significant body of research that has resulted in sophisticated robots and painting machines, together with specialized algorithms mimicking particular artistic techniques. The resulting setups are often expensive and complex, making them unavailable for recreational and hobbyist use. In recent years, however, a new class of affordable low‐cost plotters and cutting machines has reached the market. In this paper, we present a novel system for the physical generation of line and cut‐out art based on digital images, targeted at such off‐the‐shelf devices. Our approach uses a meta‐optimization process to generate results that represent the tonal content of a digital image while conforming to the physical and mechanical constraints of home‐use devices. By flexibly combining basic sets of positional and shape encodings, we are able to recreate a wide range of artistic styles. Furthermore, our system optimizes the output in terms of visual perception based on the desired viewing distance, while remaining scalable with respect to the medium size.

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“…Soon after the publication of the original work, various changes and improvements were proposed. One of these is to replace the Laplace operator by the biharmonic operator, typically yielding smoother results [FSH11;Jes16]. Other contributions include the concepts of barrier curves [Bez+10] and diffusion points [FSH11].…”

Section: Improvementsmentioning

confidence: 99%

Splines for engineers: with selected applications in numerical methods and computer graphics

Barendrecht

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Spiro splines [Lev09] are an interesting alternative for font design and are available in FontFoRge and InKscape. ‡ Two of these attributes are kerning and ligatures, which are both used extensively by X Ǝ T E X. Spotting ligatures in a text is an enjoyable game and often provides a reasonable indication of what a font has to offer! 13 2.1 The above might raise the question whether composite curves connecting with e.g. C 1 continuity can be represented more efficiently, as the middle of these three co-linear points is merely a convex combination of the other two. The answer is positive and can be obtained by studying B-spline curves. 2.1.2 B-spline curves B-splines † come in many different flavours, can be defined using a variety of ways, and form an extensive area of research. Merely interpreting them as an efficient way to represent composite Béziers does perhaps not do them justice, but as this is the direction we come from, it is our starting point. An important aspect to consider when connecting Bézier curves is whether all segments should be defined on parameter intervals of the same length. If we choose to do so, and set that interval to be of unit length, we obtain a vector of parameter values Ξ = [0, 1, 2,. .. , m], where m indicates the number of segments. These parameter values indicate where our segments are connected, or tied together, in parameter space. For this reason, they are often referred to as knots, and Ξ as the knot-vector. Let us consider a composite quadratic Bézier curve of two segments that connect with C 1 continuity. We thus have control points P 0 ,. .. , P 4 , with as corresponding basis functions M 0 (t),. .. , M 4 (t) the Bernsteins, which for the second curve segment are shifted by one unit: M 0 (t) = (1 − t) 2 for t ∈ [0, 1], M 1 (t) = 2t(1 − t) for t ∈ [0, 1], M 2 (t) = t 2 (2 − t) 2 for t ∈ [0, 1], for t ∈ [1, 2], M 3 (t) = 2(t − 1)(2 − t) for t ∈ [1, 2], M 4 (t) = (t − 1) 2 for t ∈ [1, 2].

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Generalized Diffusion Curves: An Improved Vector Representation for Smooth‐Shaded Images

Cited by 14 publications

References 25 publications

Depth-aware image vectorization and editing

Depth-aware image vectorization and editing

LinesLab: A Flexible Low‐Cost Approach for the Generation of Physical Monochrome Art

Splines for engineers: with selected applications in numerical methods and computer graphics

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