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The accessibility and advancement of digital image editing tools have enabled individuals to manipulate and create realistic images without a real basis, leading to novel forms of creative expression and new professions. However, this also raises concerns over the malicious use of these technologies in spreading disinformation and fabricated evidence. Deepfake videos, which are generated using deep learning techniques, have become a major concern due to their potential to spread false information and cause harm to individuals and society as a whole. Therefore, the development of accurate and efficient deepfake detection methods has become an urgent need. After a thorough review of deep learning-based approaches for detecting deepfake videos, the LRNet method was chosen as a basis for further research due to its high precision. The method is designed to analyze the temporal changes in a video and identify whether the video has been manipulated or not. Experiments were conducted using a publicly available dataset. The first step involved analyzing the impact of model parameters. A total of 135 combinations were analyzed by changing the block size, dropout rate, learning rate, and optimizer. Based on the results, the model's performance was enhanced by reducing the initial dropout rate, decreasing the number of GRU hidden neurons, and adding additional linear and ReLU6 layers. Upon conducting and comparing the results, it becomes evident that the chosen and improved method achieves promising outcomes in deepfake detection. This demonstrates the effectiveness of the dual-stream RNNs and the calibration module in enhancing the accuracy of geometric feature detection over time. This approach offers a more reliable way to detect deepfake videos, which is essential for preventing their malicious use in various domains. The results show that our proposed improved method achieves higher accuracy in some scenarios and provides a valuable analysis on how detection models are affected by their parameters. [ABSTRACT FROM AUTHOR]

• Most latent prints are edited by examiners in some manner, although techniques vary. • Image editing improves print quality and clarity, as defined by objective quality metrics. • Latent print examiners vary in their ability to improve the clarity of print images. • Image editing procedures would benefit from formal guidance or standard procedures. Field research within latent print comparison has remained sparse in the context of an otherwise growing body of literature examining the discipline. Studies examining how ACE-V procedures are implemented within active crime laboratories are especially lacking in light of research suggesting significant variability in examiner practices despite standardized ACE-V procedures. To date, no studies have examined a potentially important aspect of the Analysis phase: digital image editing. We provide information on the prevalence and types of latent print image editing within one laboratory (i.e., Houston Forensic Science Center), examine the potential effect of image editing on objective print quality and clarity (i.e., LQMetrics scores), and explore potential examiner differences in editing effectiveness. Results indicate that most latent prints are edited in some manner, and that image editing improves the quality and clarity of print images as defined by an objective quality metric, although examiners varied in their ability to improve the clarity of print images. Findings suggest that formal guidance or documentation of standard editing procedures would likely improve the reliability of examiner conclusions early in the latent print comparison process. [ABSTRACT FROM AUTHOR]

Inpainting techniques, rooted in ancient art restoration practices, have become essential tools for digital image editing in modern contexts. Despite their widespread applications across diverse domains, the rapid advance of inpainting methodologies has highlighted the need for comprehensive reviews to document progress and identify areas for deeper investigation. Although there are many works in literature describing the state of the art regarding inpainting methods, algorithms, and technologies, many of them are presented lacking methodological rigor, which compromises the reliability and validity of their conclusions. In light of the wide literature about inpainting, this tertiary review aims to systematically identify their main techniques, recurring challenges, and applications through the perspective of secondary studies, providing a helpful background for new researchers. Our findings are based on an analysis of 45 reviews, where one of the major issues observed was the lack of standardization in the classification of methods, and to address this, we provide a concise and clear classification. Furthermore, we present a summary of the most commonly used metrics and a discussion of the main shortcomings and applications, which extend beyond digital image restoration to include medical imaging, three-dimensional restoration, cultural heritage preservation, and more. While inpainting poses challenges, this review aims to inspire further exploration and advancement in the field by providing a comprehensive overview of inpainting research. [Display omitted] • This study provides a comprehensive tertiary literature review on inpainting. • We discuss the common challenges and gaps in the current inpainting landscape. • We enumerate the most used metrics to evaluate inpainting results. [ABSTRACT FROM AUTHOR]

With the expeditious advancement in digital technology and image editing software, it has become easy to manipulate digital images. Copy-move is a common type of image forgery, which threatens the authenticity of digital images by copying and pasting a certain part of the image within the same image. The main focus of this paper is to detect single as well as multiple copy-move forgeries efficiently by combining block-based and keypoint-based detection approaches. The fusion of block-based detection techniques i.e. adaptive over-segmentation (AS) and keypoint-based detection techniques i.e. accelerated KAZE (AKAZE) and scale-invariant feature transform (SIFT) makes the proposed scheme robust against various geometrical attacks as well as less computationally expensive. Moreover, the input image is converted into the different color channels and then, Cr channel is used for further processing because it detects the tampering artifacts left in the image which cannot be observed by human eyes. Also, the copy-move forgery is detected more precisely even in smooth regions due to the extraction of an adequate number of key points. The experimental results are executed on MICC-F220, IMD, GRIP, and COVERAGE datasets, and various performance metrics like precision, recall, F1 score, and F2 score are evaluated. The experimental results show that the proposed technique is robust against various geometrical attacks i.e. rotation, scaling, JPEG compression, and noise addition, and proved better when compared with the other existing techniques. Moreover, to ensure the robustness of the proposed approach, the statistical analysis test using ANOVA and cross-dataset performance is evaluated. [ABSTRACT FROM AUTHOR]

In recent years, the protection of the intellectual property rights of digital media has become a considerable issue. Especially using digital image editing tools has made it very easy and fast to manipulate images. Therefore, manipulation detection of digital images has become a necessity. This article presents a novel Frei‐Chen based self‐embedding fragile watermarking technique implemented to 3×3 blocks for image manipulate detection. The block key and the Frei‐Chen based block feature are calculated from the non‐overlapping image blocks of size 3×3. Exclusive‐OR operations are applied to the Frei‐Chen based block feature and the block key. After, a nine bit block authentication key is generated from the Frei‐Chen based block feature and the block key. Then the generated authentication key is embedded in the least significant bits of each block. Experimental results prove the effectiveness of the proposed method through the detection of the various attacks and obtain the excellent visual quality of watermarked images. Also, the results demonstrate that the proposed method detects all of the manipulated areas plainly. [ABSTRACT FROM AUTHOR]

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With the rapid development of multimedia technology, editing and manipulating digital images have become more accessible than ever. This paper proposed color image authentication based on blind fragile image watermarking for tamper detection and self-recovery named AuSR1. The AuSR1 divides each channel of the cover image into non-overlapping blocks with the size of 2 × 2 pixels. The authentication data is embedded into the original block location, while the recovery data is embedded into the distant location from the original location based on the block mapping algorithm. The watermark data is then embedded into the 2 LSB to achieve high quality of the recovered image under tampering attacks. In addition, the permutation algorithm is applied to ensure the security of the watermark data. The AuSR1 utilizes a three-layer authentication algorithm to achieve a high detection rate. The experimental results show that the scheme produced a PSNR value of 45.57 dB and an SSIM value of 0.9972 of the watermarked images. Furthermore, the AuSR1 detected the tampered area of the images with a high precision value of 0.9943. In addition, the recovered image achieved a PSNR value of 27.64 dB and an SSIM value of 0.9339 on a 50% tampering rate. [ABSTRACT FROM AUTHOR]

PURPOSE. The present study aims to analyze the effect of abutment neck taper and types of cement on the amount of undetected remnant cement of cementretained implant prostheses. MATERIALS AND METHODS. Three neck taper angles (53°, 65°, 77°) and three types of cement (RMGI: resin-modified glass ionomer, ZPC: zinc phosphate cement, ZOE: zinc oxide eugenol cement) were used. For each group, the surface percentage was measured using digital image and graphic editing software. The weight of before and after removing remnant cement from the abutment-crown assembly was measured using an electronic scale. Two-way ANOVA and Duncan & Scheffe's test were used to compare the calculated surface percentage and weight of remnant cement (α = .05). RESULTS. There were significant differences in remnant cement surface percentage and weight according to neck taper angles ( P < .05). However, there were no significant differences in remnant cement surface percentage and weight on types of cement. No interaction was found between neck taper angles and types of luting cement ( P > .05). The wide abutment with a small neck taper angle showed the most significant amount of remnant cement. And the types of luting cement did not influence the amount of residual cement. CONCLUSION. To remove excess cement better, the emergence profile of the crown should be straight to the neck taper of the abutment in cement-retained implant restoration. [ABSTRACT FROM AUTHOR]

With the proliferation of smartphones and social networking services, the opportunities for individuals to take photographs have increased exponentially. In a previous study, the perceived gloss of an object was reduced by its representing as a digital image and compared with a real object. It is also known that image editing, such as lossy image compression, can reduce the glossiness of an image. Therefore, the glossiness of real objects may be easily changed in digital images; thus, a method for appropriately editing the gloss in digital images is required for post-processing. In this study, we propose a gloss appearance editing method for various material objects in a single digital image. The proposed method consists of three steps: color space conversion, gloss detection, and gloss editing. The relationship between the proposed method and the respective reflection models of inhomogeneous objects, metallic objects, and translucent objects was analyzed. Consequently, we determined that the gloss editing of the proposed method is equivalent to editing the specular reflection component of an inhomogeneous object, the grazing reflection component of a metallic object, and the specular reflection component of a translucent object. We applied the proposed method to test images including objects of various materials and confirmed its effectiveness through a subjective evaluation by visual inspection and an objective evaluation using image statistics. [ABSTRACT FROM AUTHOR]

Indigenous photobomb memes emerged on social networks as a media practice alongside contemporary activist campaigns, where artists insert pop culture content into digitized ethnographic photographs already in use as mainstream meme fodder. This article takes a materialist approach to such memes to explore how the technical processes of digital image editing function ideologically. Meme series by Kiowa-Choctaw artist Steven Paul Judd and others illustrate how compositing methods like cloning and healing tools may disrupt ethnographic photographs' claims to history, interrogating the aesthetic systems that underwrite settler-colonial media. As these algorithmic processes remediate the digitized image and re-situate it relative to other photoshopping practices, they bear a trace of settler digitality that allows such memes to intervene in current cultural debates and aesthetic trends. Circulation via social media generates a web of twice-remediated memes, which always refer back to their prior analog and digital iterations. [ABSTRACT FROM AUTHOR]

Eyewitness identification is a notoriously unreliable form of evidence in criminal trials, yet juries tend to accord significant weight to the testimony of eyewitnesses. This concern is at the forefront of modern efforts to reform eyewitness identification procedure and reduce the risk of misidentification and wrongful conviction. The U.S. Supreme Court has historically recognized limited constitutional protections against unnecessarily suggestive eyewitness identification procedures, such as the use of photo lineups where the suspect's photo clearly stands out to the witness. This poses a challenge for law enforcement when a suspect has uniquely identifying physical characteristics, and similar filler photos are impractical or impossible to obtain. Law enforcement agencies increasingly rely on modern tools like image editing software to ensure uniformity across photo lineups. Many agencies now use image editing programs to add, edit, or remove identifying physical characteristics from a suspect's photo. This can increase the risk of misidentification, particularly when the edits are made to better match a description of the culprit provided by a witness. Because existing law does not sufficiently regulate the use of image editing software in photo-based identification procedures, this Note proposes model language for state legislatures to adopt in a statute prohibiting the practice of making material edits to a suspect's photo for use in eyewitness identification. [ABSTRACT FROM AUTHOR]

In this paper, the authors present the initial findings from explorations on transformation patterns of data in raw format when crossing or transmediating directly (i.e. unaffected by any other form of codification) between audio and visual media. These patterns have allowed the authors to engage in the production of transmediatic artifacts with some degree of control and agency, facilitating purposeful applications of transmediation. The products of such practices will enable a form of literacy, an aesthetic means to identify in visual media artifacts those patterns that could transmediate into useful or appealing sonic artifacts and vice versa. [ABSTRACT FROM AUTHOR]

Although image inpainting, or the art of repairing the old and deteriorated images, has been around for many years, it has recently gained even more popularity, because of the recent development in image processing techniques. With the improvement of image processing tools and the flexibility of digital image editing, automatic image inpainting has found important applications in computer vision and has also become an important and challenging topic of research in image processing. This paper reviews the existing image inpainting approaches, that were classified into three subcategories, sequential-based, CNN-based, and GAN-based methods. In addition, for each category, a list of methods for different types of distortion on images are presented. Furthermore, the paper also presents available datasets. Last but not least, we present the results of real evaluations of the three categories of image inpainting methods performed on the used datasets, for different types of image distortion. We also present the evaluations metrics and discuss the performance of these methods in terms of these metrics. This overview can be used as a reference for image inpainting researchers, and it can also facilitate the comparison of the methods as well as the datasets used. The main contribution of this paper is the presentation of the three categories of image inpainting methods along with a list of available datasets that the researchers can use to evaluate their proposed methodology against. [ABSTRACT FROM AUTHOR]

• U2-net and Trans-GAN are used as generators to extract and generate facial attributes. • Parallel generation countermeasure improves real and generated image similarity. • Semantic consistency and circular consistency loss enhance editing of attributes. • Semantic segmentation, attribute mask separation, background mask improve quality. Facial attribute editing encounters problems of incorrect changes to face regions and artifacts in generated images. We propose a facial attribute editing method combined with parallel GAN for attribute separation. First, the method integrates the U2-net encoder and Trans-GAN decoder as a model encoder to extract and generate facial spatial information effectively. Second, RGB images and semantic mask images are used to train a parallel generator and discriminator respectively. Semantic consistency loss is introduced to ensure that the two branches have consistent semantic output and achieve the effect of convergence in the same direction parallel generator and discriminator. The proposed model, trained on the CelebAMask-HQ original dataset and verified by the CelebA dataset, adopts the separation of the face mask image and the background mask image, to improve the correct rate of face attribute editing. Compared with existing facial attribute editing methods, the proposed method is capable of balancing attribute editing ability and details preservation ability. It can accurately edit the target attribute area and greatly improve the quality of facial images. [ABSTRACT FROM AUTHOR]

There are strict guidelines on photoediting in newsrooms and serious professional repercussions for any failure to adhere to them, while computer-generated imagery is increasingly used in other areas of visual communication. This article presents empirical research on the ability of professional photographers and editors to distinguish photographs from photorealistic computer-generated images by looking at them on a screen. The results show clearly that those studied (N = 20) are unable to distinguish one from another, suggesting that it is increasingly difficult to make this distinction, particularly since most viewers are not as experienced in photography as those studied. Interestingly, the participants continue to share a conventional understanding of photography that is not in line with current developments in digital photography and digital image rendering. Based on their findings, the authors suggest there is a need for developing a particular visual literacy that understands the computational in digital photography and grounds the use of digital photography among particular communities of practice. When seeing photographs on screens, journals, exhibitions, or newspapers, viewers might actually be looking at computer-generated simulations, and vice versa. [ABSTRACT FROM AUTHOR]

The ability to quickly and intuitively edit digital content has become increasingly important in our everyday life. However, existing edit propagation methods for editing digital images are typically based on optimization with high computational cost for large inputs. Moreover, existing edit propagation methods are generally inefficient and highly time-consuming. Accordingly, to improve edit efficiency, this paper proposes a novel edit propagation method using a bilateral grid, which can achieve instant propagation of sparse image edits. Firstly, given an input image with user interactions, we resample each of its pixels into a regularly sampled bilateral grid, which facilitates efficient mapping from an image to the bilateral space. As a result, all pixels with the same feature information (color, coordinates) are clustered to the same grid, which can achieve the goal of reducing both the amount of image data processing and the cost of calculation. We then reformulate the propagation as a function of the interpolation problem in bilateral space, which is solved very efficiently using radial basis functions. Experimental results show that our method improves the efficiency of color editing, making it faster than existing edit approaches, and results in excellent edited images with high quality. [ABSTRACT FROM AUTHOR]

Digital images and video are the basic media for communication nowadays. They are used as authenticated proofs or corroboratory evidence in different areas like: forensic studies, law enforcement, journalism and others. With development of software for editing digital images, it has become very easy to change image content, add or remove important information or even to make one image combining multiple images. Thus, the development of methods for such change detection has become very important. One of the most common methods is copy-move forgery detection (CMFD). Methods of this type include change detection that occur by copying a part of an image and pasting it to another location within the image. We propose new method for detection of such changes using certain multifractal parameters as characteristic features, as well as common statistical parameters. Before the analysis, images are divided into non-overlapping blocks of fixed dimensions. For each block, the characteristic features are calculated. In order to classify observed blocks, we used metaheuristic method and proposed new semi-metric function for similarity analysis between blocks. Simulation shows that the proposed method provides good results in terms of precision and recall, with low computational complexity. [ABSTRACT FROM AUTHOR]

In recent years, tampering and altering of digital images have become easier with the rapid development of computer technologies such as digital image editing tools. Therefore, verification of image integrity and tamper detection of digital images have become a great challenge. Fragile watermarking is the most widely used method for protecting the integrity and content authenticity of the image. In this paper, by using SHA-256 hash function, a novel block based fragile watermark embedding and tamper detection method is proposed. In watermark embedding phase, host image is divided into 32 × 32 non-overlapped blocks. Each 32 × 32 block is then divided into four 16 × 16 nonoverlapped sub-blocks. The entire hash value of the first three sub-blocks is generated as a watermark using SHA-256 hash function. The generated 256-bit binary watermark is embedded into the least significant bits (LSBs) of the fourth sub-block and watermarked image is obtained. In tamper detection phase, the detection of tampered block has been performed by comparing the hash value obtained from the three sub-blocks with the extracted watermark from the fourth sub-block of the watermarked image. The performance of the proposed method has been evaluated by applying linear and nonlinear attacks to the different regions of the watermarked images. Experimental results show that the proposed method detects all the tampered regions of the attacked images and high visual quality of watermarked images has been obtained. [ABSTRACT FROM AUTHOR]

When motion capture data is applied to virtual characters, the applied motion often exhibits geometric and physical errors, which necessitates a cumbersome refinement process. We present a novel framework to efficiently obtain a corrected motion as well as its supporting contact information from multi-contact motion capture data. To this end, first, we present a projective dynamics-based method for optimizing character motions. By carefully defining objective functions and constraints using differential representation of motions, we develop a highly efficient motion optimizer that can create geometrically and dynamically adjusted motions given reference motion data and contact information. Second, we develop a contact optimizer that finds a set of contacts that allows the motion optimizer to generate a motion that best follows the reference motion under dynamic and geometric constraints. This is achieved by iteratively improving the hypothesis on the best set of contacts by getting feedback from the motion optimizer. We demonstrate that our method significantly improves the naturalness of a wide range of motion capture data, from walking to rolling. [ABSTRACT FROM AUTHOR]

Maliciously edited images, also referred to as tampered or forged images, have become ubiquitous and challenging in recent times with the advent of social media platforms. Image splicing is a kind of image tampering where regions of images are copied and pasted into another image. Image tampering detection is a method for the authenticity verification of images produced as evidence in the court of law and forms a sub problem in image forensics. The aim of our work is to detect and locate the boundaries of image splicing, without a-priori knowledge of the reference image. We propose two methods, of which the first uses classification of texture patterns along with the standard deviations of block discrete cosine transformation of textures. In the second method, we combine the first with image quality artifacts incurred due to image tampering along with the entropy of histograms to get an integrated method. We use a support vector machine classifier for training and testing these approaches. Our methods are tested on two publicly available tamper detection datasets and the results are compared with seven other existing works. It is observed that our integrated method gives best results. We have also tested the proposed methods on a social media dataset and the results are encouraging. [ABSTRACT FROM AUTHOR]

Taking into consideration that the prior CMF detection methods rely on several fixed threshold values in the filtering process, we propose an efficient CMF detection method with an automatic threshold selection, named as CMF-iteMS. The CMF-iteMS recommends a PatchMatch-based CMF detection method that adapts Fourier-Mellin Transform (FMT) as the feature extraction technique while a new automatic threshold selection based on iterative means of regions size (iteMS) procedure is introduced to have flexibility in changing the threshold value for various characteristics (quality, sizes, and attacks) in each input image. To ensure the reliability of the proposed CMF-iteMS, the method is compared with four state-of-the-art CMF detection methods based on Scale Invariant Feature Transform (SIFT), patch matching, multi-scale analysis and symmetry techniques using three available datasets that cover the variety of characteristics in CMF images. The results show that the F-score of the CMF-iteMS outperformed existing CMF detection methods by exceeding an average of 90% F-score values for image-level evaluation and 82% of F-score value for pixel-level evaluation for all datasets in original size. As special attention is given to the image resizing attack, the method is able to maintain the highest performance even if the images in the datasets are resized to 0.25 parameter. [ABSTRACT FROM AUTHOR]

Building a human‐centered editable world can be fully realized in a virtual environment. Both mixed reality (MR) and virtual reality (VR) are feasible solutions to support the attribute of edition. Based on the current development of MR and VR, we present the vision‐tangible interactive display method and its implementation in both MR and VR. We address the issue of MR and VR together because they are similar regarding the proposed method. The editable mixed and virtual reality system is useful for studies, which exploit it as a platform. In this paper, we construct a virtual reality environment based on the Oculus Rift, and an MR system based on a binocular optical see‐through head‐mounted display. In the MR system about manipulating the Rubik's cube, and the VR system about deforming the virtual objects, the proposed vision‐tangible interactive display method is utilized to provide users with a more immersive environment. Experimental results indicate that the vision‐tangible interactive display method can improve the user experience and can be a promising way to make the virtual environment better. Building a human‐centered editable world can be fully realized in a virtual environment. Both mixed reality and virtual reality are feasible solutions to support the attribute of being editable. Based on the current development of mixed reality (MR) and virtual reality (VR), we present the vision‐tangible interactive display method and its implementation in both MR and VR. [ABSTRACT FROM AUTHOR]

This section presents a correction to the article "Deepfakes and Digitally Altered Imagery Abuse: A Cross-Country Exploration of an Emerging form of Image-Based Sexual Abuse," published in a previous issue.

Abstract The paper describes displacement measurements taken in the vicinity of a fatigue crack tip using digital image correlation. In-situ loading is employed in a scanning electron microscope to get measurements very close to the tip. The results are compared to the usual elastic model of crack tip deformation and to the Christopher, James and Patterson model, which is critically discussed. It is shown that the use of an elastic model with a residual stress intensity caused by crack tip shielding gives a good representation of the experimental results. [ABSTRACT FROM AUTHOR]

Image color editing techniques are of great significance for users who wish to adjust the image color. However, previous works paid less attention to the translucent images. In this paper, we propose a new method to recolor the translucent images while preserving detailed information and color relationships of the source image. We consider the recolor problem as a location transformation problem and solve it in two steps: automatic palette extraction and homography estimation. First, we propose the Hmeans method to extract the dominant colors of the source image based on histogram statistics and clustering. Then, we propose homography estimation to map the source colors to desired colors in the CIE‐LAB color space. Further, we adopt a non‐linear optimization approach to improve the result generated by the last step. The proposed method maintains high fidelity of the source image. Experiments have shown that our method generates a state‐of‐the‐art visual result, in particular in the shadow areas. The source images with ground truth generated by a ray tracer further verify the effectiveness of our method. [ABSTRACT FROM AUTHOR]

A narrative collage is an interesting image editing method for summarizing the main theme or storyline behind an image collection. We present a novel method to generate narrative images with plausible semantic scene structures. To achieve this goal, we introduce a layer graph and a scene graph to represent the relative depth order and semantic relationship between image objects, respectively. We first cluster the input image collection to select representative images, and then we extract a group of semantic salient objects from each representative image. Both layer graphs and scene graphs are constructed and combined according to our specific rules for reorganizing the extracted objects in every image. We design an energy model to appropriately locate every object on the final canvas. The experimental results show that our method can produce competitive narrative collage results and that it performs well on a wide range of image collections. [ABSTRACT FROM AUTHOR]

This paper presents a novel GPU-based patch matching method which efficiently finds approximate nearest neighbor correspondences for patches between images. Our approach improves traditional patch matching algorithms in two aspects. First, we propose to improve the convergence of matching with two new types of forward enrichment operations, enabling the fast propagation of a richer set of potentially good candidates on different images. Second, we reduce the search space of patch direction by estimating a coherent feature direction field for each image and computing the similarity between patches with a direction-aware alignment scheme. Furthermore, we develop a number of GPU-based image editing and processing applications by incorporating our new patch matching algorithm, including object matching, nonlocal means denoising, image completion, texture synthesis, and image retargeting. Experimental results and comparisons are shown to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a method for fitting digital hyperspheres to a given set of n D points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. The digital Hyperspheres are defined using the k -Flake Digitization models [25] . We present an algorithm, that provides optimal fitting solutions for digital k -Flake hyperspheres within a time complexity O ( ( ( n k ) 2 n − k ) n N n + 1 log ⁡ N ) for dimension n , N being the number of points. We have implemented this algorithm for the particular case of 3D 2-Flake spheres that corresponds to the classical so called Naive digital spheres. [ABSTRACT FROM AUTHOR]

We present a novel system for sketch-based face image editing, enabling users to edit images intuitively by sketching a few strokes on a region of interest. Our interface features tools to express a desired image manipulation by providing both geometry and color constraints as user-drawn strokes. As an alternative to the direct user input, our proposed system naturally supports a copy-paste mode, which allows users to edit a given image region by using parts of another exemplar image without the need of hand-drawn sketching at all. The proposed interface runs in real-time and facilitates an interactive and iterative workflow to quickly express the intended edits. Our system is based on a novel sketch domain and a convolutional neural network trained end-to-end to automatically learn to render image regions corresponding to the input strokes. To achieve high quality and semantically consistent results we train our neural network on two simultaneous tasks, namely image completion and image translation. To the best of our knowledge, we are the first to combine these two tasks in a unified framework for interactive image editing. Our results show that the proposed sketch domain, network architecture, and training procedure generalize well to real user input and enable high quality synthesis results without additional post-processing. [ABSTRACT FROM AUTHOR]