360°depth estimation is a challenging research problem due to the difficulty of finding a representation that both preserves global continuity and avoids distortion in spherical images. Existing methods attempt to leverage complementary information from multiple projections, but struggle with balancing global and local consistency. Their local patch features have limited global perception, and the combined global representation does not address discrepancies in feature extraction at the boundaries between patches. To address these issues, we propose Cross360, a novel cross-attention-based architecture integrating local and global information using less-distorted tangent patches along with equirectangular features. Our Cross Projection Feature Alignment module employs cross-attention to align local tangent projection features with the equirectangular projection's 360° field of view, ensuring each tangent projection patch is aware of the global context. Additionally, our Progressive Feature Aggregation with Attention module refines multi-scaled features progressively, enhancing depth estimation accuracy. Cross360 significantly outperforms existing methods across most benchmark datasets, especially those in which the entire 360° image is available, demonstrating its effectiveness in accurate and globally consistent depth estimation. The code and model are available at https://github.com/huangkun101230/Cross360.

Omnidirectional capture of dynamic scenes facilitates the creation of immersive virtual reality assets and holistic scene understanding. Outward-facing multi-fisheye camera rigs offer an efficient solution for full-scene coverage, using fewer lenses than conventional pinhole arrays while enabling all-directional observation of complex, time-varying environments. By continuously recording scene evolution from every angle, these systems naturally enable a richer characterization of dynamic interactions. Despite these advantages, dynamic scene modeling in this setting remains underexplored. Existing methods, typically designed for fixed pinhole configurations or monocular setups, rely heavily on photometric cues and often neglect the strong geometric and semantic priors inherent in multi-fisheye omnidirectional data. To address this gap, we present OmniPrior, a Gaussian Splatting-based framework for outward-facing, multi-fisheye omnidirectional capture. Our approach incorporates metric-geometry-aware initialization with multi-prior guidance, introducing a dynamicness-aware Gaussian representation that encodes both object motion and subtle temporal variations. The resulting representations are physically consistent and temporally stable. Extensive experiments validate the effectiveness of our method in novel view synthesis across new viewpoints and timestamps. We demonstrate its utility in two representative applications derived from our learned representations: 6DoF rendering with flexible FoV and motion-freeze rendering.

360° images have wide applications in fields such as virtual reality and user experience design. Our goal is to adjust these images to guide users' visual attention. To achieve this, we present a novel task: target scanpath-guided 360° image enhancement, which aims to enhance 360° images based on user-specified target scanpaths. We develop a Progressive Scanpath-Guided Enhancement Method (PSEM) to address this problem through three stages. In the first stage, we propose a Time-Alignment and Spatial Similarity Clustering (TASSC) algorithm that accounts for the spherical nature of 360° images and the temporal dependency of scanpaths to generate representative scanpaths. In the second stage, we learn the differences between the source and the target scanpaths and select the objects to be edited based on these differences. Particularly, we propose a Dual-Stream Scanpath Difference Encoder (DSDE) embedded into the Segment Anything Model (SAM) network for object mask generation. Finally, we employ a Stable Diffusion network fine-tuned with LoRA technology to produce the final enhanced image. Additionally, we design special loss functions to supervise the training of the second and third stages. Experimental results have demonstrated the effectiveness of our approach for scanpath-guided 360° image enhancement.

Consumer-level omnidirectional video offers an economically viable means to create virtual reality (VR) assets, enabling users to explore and interact within a fully immersive visual environment. However, editing such videos, particularly those with 360${}^{\circ }$∘ views and dynamic objects, poses significant challenges. Existing approaches to representing and manipulating omnidirectional content-whether designed for typical 2D perspective imagery or panoramas-often fail to adequately capture the complex spatiotemporal relationships crucial for producing high-quality, editable outputs in dynamic, panoramic settings. To overcome these challenges, we introduce OmniPlane, a novel method that leverages spherical spatiotemporal feature grids to empower the representation and editability of real-world dynamic omnidirectional environments casually captured by commodity omnidirectional cameras. OmniPlane computes spatiotemporal features by fusing vectors or matrices from each learnable spatial and spatiotemporal feature plane within a spherical coordinate system, complemented by a specifically designed weighted sampling strategy respecting the inherent spherical distribution of omnidirectional content. These learned feature planes can be flexibly decomposed into palette-based color bases. This innovative method not only enhances the representation capability of omnidirectional content and dynamics but also enables the recoloring of omnidirectional videos. Extensive experiments and a dedicated user study validate the superior performance of our proposed method in facilitating recolorable representations of dynamic omnidirectional environments.

Content-based 360° video editing allows users to manipulate panoramic content for interaction in a dynamic visual world. However, the current related methods (2D neural representation and optical flow) show limitations in producing high-quality panoramic content from 360° videos due to their lack of capacity to model the inherent spatiotemporal relationships among pixels in the true panoramic space. To address this issue, we propose a Neural Panoramic Representation (NPR) method to model the global inter-pixel relationships, facilitating immersive video editing. Specifically, our method utilizes MLP-based networks to learn spherical implicit content layers, by encoding the spherical spatiotemporal positions and appearance details within the panoramic video, and bi-directional mapping between the original video frames and the learned content layers, to capture the interpretable and global omnidirectional visual characteristics of individual dynamic scenes. Additionally, we introduce innovative loss functions (spherical neighborhood consistency and unit spherical regularization) to ensure the creation of appropriate implicit spherical content layers. We further provide an interactive layer neural panoramic editing approach based on the proposed NPR, in the head-mounted display device. We evaluate this framework on diverse real-world 360° videos, showing superior performance on both reconstruction and consistent editing compared to existing state-of-the-art (SOTA) neural representation techniques.

Scanpath generation in 360° images aims to model the realistic trajectories of gaze points that viewers follow when exploring panoramic environments. Existing methods for scanpath genera- tion suffer from various limitations, including a lack of global atten-tion to panoramic environments, insufficient diversity in generated scanpaths, and inadequate consideration of the temporal sequence of gaze points. To address these challenges, we propose a novel approach, named ScanTD, which employs a conditional Diffusion Model-based method to generate multiple scanpaths. Notably, a transformer-based time-series (TTS) module with a novel attention mechanism is integrated into ScanTD to capture the temporal de- pendency of gaze points effectively. Additionally, ScanTD utilizes a Vision Transformer-based method for image feature extraction, en- abling better learning of scene semantic information. Experimental results demonstrate that our approach outperforms state-of-the-art methods across three datasets. We further demonstrate its general- izability by applying it to the 360° saliency detection task.

360° images and videos have become an economic and popular way to provide VR experiences using real-world content. However, the manipulation of the stereo panoramic content remains less explored. In this paper, we focus on the 360° image composition problem, and develop a solution that can take an object from a stereo image pair and insert it at a given 3D position in a target stereo panorama, with well-preserved geometry information. Our method uses recovered 3D point clouds to guide the composited image generation. More specifically, we observe that using only a one-off operation to insert objects into equirectangular images will never produce satisfactory depth perception and generate ghost artifacts when users are watching the result from different view directions. Therefore, we propose a novel per-view projection method that segments the object in 3D spherical space with the stereo camera pair facing in that direction. A deep depth densification network is proposed to generate depth guidance for the stereo image generation of each view segment according to the desired position and pose of the inserted object. We finally combine the synthesized view segments and blend the objects into the target stereo 360° scene. A user study demonstrates that our method can provide good depth perception and removes ghost artifacts. The per-view solution is a potential paradigm for other content manipulation methods for 360° images and videos.

We investigate the optimal aesthetic location and size of a single dominant salient region in a photographic image. Existing algorithms for photographic composition do not take full account of the spatial positioning or sizes of these salient regions. We present a set of experiments to assess aesthetic preferences, inspired by theories of centeredness, principal lines, and Rule-of-Thirds. Our experimental results show a clear preference for the salient region to be centered in the image and that there is a preferred size of non-salient border around this salient region. We thus propose a novel image cropping mechanism for images containing a single salient region to achieve the best aesthetic balance. Our results show that the Rule-of-Thirds guideline is not generally valid but also allow us to hypothesize in which situations it is useful and in which it is inappropriate.

We report two studies that investigate the use of subjective believability in the assessment of objective realism of terrain. The first demonstrates that there is a clear subjective feature bias that depends on the types of terrain being evaluated: Our participants found certain natural terrains to be more believable than others. This confounding factor means that any comparison experiment must not ask participants to compare terrains with different types of features. Our second experiment assesses four methods of example-based terrain synthesis, comparing them against each other and against real terrain. Our results show that, while all tested methods can produce terrain that is indistinguishable from reality, all also can produce poor terrain; that there is no one method that is consistently better than the others; and that those who have professional expertise in geology, cartography, or image analysis are better able to distinguish real terrain from synthesized terrain than the general population, but those who have professional expertise in the visual arts are not.

Abstract Gradient meshes are a 2D vector graphics primitive where colour is interpolated between mesh vertices. The current implementations of gradient meshes are restricted to rectangular mesh topology. Our new interpolation method relaxes this restriction by supporting arbitrary manifold topology of the input gradient mesh. Our method is based on the Catmull‐Clark subdivision scheme, which is well‐known to support arbitrary mesh topology in 3D. We adapt this scheme to support gradient mesh colour interpolation, adding extensions to handle interpolation of colours of the control points, interpolation only inside the given colour space and emulation of gradient constraints seen in related closed‐form solutions. These extensions make subdivision a viable option for interpolating arbitrary‐topology gradient meshes for 2D vector graphics.

NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user’s interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

CAD models generally consist of multiple NURBS patches, both trimmed and untrimmed. There is a long-standing challenge that trimmed NURBS patches cause unavoidable gaps in the model. We address this by converting multiple NURBS patches to a single untrimmed NURBS-compatible subdivision surface in a three stage process. First, for each patch, we generate in domain space a quadrangulation that follows boundary edges of the patch and respects the knot spacings along edges. Second, the control points of the corresponding subdivision patch are computed in model space. Third, we merge the subdivision patches across their common boundaries to create a single subdivision surface. The converted model is gap-free and can maintain inter-patch continuity up to C2.

Convolutional neural networks have been successfully used to compute shape descriptors, or jointly embed shapes and sketches in a common vector space. We propose a novel approach that leverages both labeled 3D shapes and semantic information contained in the labels, to generate semantically-meaningful shape descriptors. A neural network is trained to generate shape descriptors that lie close to a vector representation of the shape class, given a vector space of words. This method is easily extendable to range scans, hand-drawn sketches and images. This makes cross-modal retrieval possible, without a need to design different methods depending on the query type. We show that sketch-based shape retrieval using semantic-based descriptors outperforms the state-of-the-art by large margins, and mesh-based retrieval generates results of higher relevance to the query, than current deep shape descriptors.

We propose a cluster-based approach to point set saliency detection, a challenge since point sets lack topological information. A point set is first decomposed into small clusters, using fuzzy clustering. We evaluate cluster uniqueness and spatial distribution of each cluster and combine these values into a cluster saliency function. Finally, the probabilities of points belonging to each cluster are used to assign a saliency to each point. Our approach detects fine-scale salient features and uninteresting regions consistently have lower saliency values. We evaluate the proposed saliency model by testing our saliency-based keypoint detection against a 3D interest point detection benchmark. The evaluation shows that our method achieves a good balance between false positive and false negative error rates, without using any topological information.

Traditionally, modelling using spline curves and surfaces is facilitated by control points. We propose to enhance the modelling process by the use of control vectors. This improves upon existing spline representations by providing such facilities as modelling with local (semi-sharp) creases, vanishing and diagonal features, and hierarchical editing. While our prime interest is in surfaces, most of the ideas are more simply described in the curve context. We demonstrate the advantages provided by control vectors on several curve and surface examples and explore avenues for future research on control vectors in the contexts of geometric modelling and finite element analysis based on splines, and B-splines and subdivision in particular.

Abstract A challenge in vector graphics is to define primitives that offer flexible manipulation of colour gradients. We propose a new primitive, called a shading curve, that supports explicit and local gradient control. This is achieved by associating shading profiles to each side of the curve. These shading profiles, which can be manually manipulated, represent the colour gradient out from their associated curves. Such explicit and local gradient control is challenging to achieve via the diffusion curve process, introduced in 2008, because it offers only implicit control of the colour gradient. We resolve this problem by using subdivision surfaces that are constructed from shading curves and their shading profiles.

We show that the error in 3D gaze depth (vergence) estimated from binocularly-tracked gaze disparity is related to the viewing distance of the screen calibration plane at which 2D gaze is recorded. In a stereoscopic (virtual) environment, this relationship is evident in gaze to target depth error: vergence error behind the screen is greater than in front of the screen and is lowest at the screen depth. In a physical environment, with no accommodation-vergence conflict, the magnitude of vergence error in front of the 2D calibration plane appears reversed, increasing with distance from the viewer.

When evaluating eye tracking algorithms, a recurring issue is what metric to use and what data to compare against. User studies are informative when considering the entire eye tracking system, however they are often unsatisfactory for evaluating the gaze estimation algorithm in isolation. This is particularly an issue when evaluating a system's component parts, such as pupil detection, pupil-to-gaze mapping or head pose estimation.

This paper introduces a novel method to convert trimmed NURBS surfaces to untrimmed subdivision surfaces with Bézier edge conditions. We take a NURBS surface and its trimming curves as input, from this we automatically compute a base mesh, the limit surface of which fits the trimmed NURBS surface to a specified tolerance. We first construct the topology of the base mesh by performing a cross-field based decomposition in parameter space. The number and positions of extraordinary vertices required to represent the trimmed shape can be automatically identified by smoothing a cross field bounded by the parametric trimming curves. After the topology construction, the control point positions in the base mesh are calculated based on the limit stencils of the subdivision scheme and constraints to achieve tangential continuity across the boundary. Our method provides the user with either an editable base mesh or a fine mesh whose limit surface approximates the input within a certain tolerance. By integrating the trimming curve as part of the desired limit surface boundary, our conversion can produce gap-free models. Moreover, since we use tangential continuity across the boundary between adjacent surfaces as constraints, the converted surfaces join with G1 continuity.

Abstract We deal with subdivision schemes based on arbitrary degree B‐splines. We focus on extraordinary knots which exhibit various levels of complexity in terms of both valency and multiplicity of knot lines emanating from such knots. The purpose of truncated multiple knot lines is to model creases which fair out. Our construction supports any degree and any knot line multiplicity and provides a modelling framework familiar to users used to B‐splines and NURBS systems.

Abstract We explore a method for generalising Pixar semi‐sharp creases from the univariate cubic case to arbitrary degree subdivision curves. Our approach is based on solving simple matrix equations. The resulting schemes allow for greater flexibility over existing methods, via control vectors. We demonstrate our results on several high‐degree univariate examples and explore analogous methods for subdivision surfaces.

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points.

Robust, accurate, real-time pupil tracking is a key component for online gaze estimation. On head-mounted eye trackers, existing algorithms that rely on circular pupils or contiguous pupil regions fail to detect or accurately track the pupil. This is because the pupil ellipse is often highly eccentric and partially occluded by eyelashes. We present a novel, real-time dark-pupil tracking algorithm that is robust under such conditions. Our approach uses a Haar-like feature detector to roughly estimate the pupil location, performs a k-means segmentation on the surrounding region to refine the pupil centre, and fits an ellipse to the pupil using a novel image-aware Random Sample Concensus (RANSAC) ellipse fitting. We compare our approach against existing real-time pupil tracking implementations, using a set of manually labelled infra-red dark-pupil eye images. We show that our technique has a higher pupil detection rate and greater pupil tracking accuracy.

Abstract Sophisticated video processing effects require both image and geometry information. We explore the possibility to augment a video camera with a recent infrared time‐of‐flight depth camera, to capture high‐resolution RGB and low‐resolution, noisy depth at video frame rates. To turn such a setup into a practical RGBZ video camera, we develop efficient data filtering techniques that are tailored to the noise characteristics of IR depth cameras. We first remove typical artefacts in the RGBZ data and then apply an efficient spatiotemporal denoising and upsampling scheme. This allows us to record temporally coherent RGBZ videos at interactive frame rates and to use them to render a variety of effects in unprecedented quality. We show effects such as video relighting, geometry‐based abstraction and stylisation, background segmentation and rendering in stereoscopic 3D.

Abstract Rigging for facial animation is an important but time‐consuming task, which generally requires experienced artists with knowledge of facial anatomy. In this paper, we investigate whether it is possible to produce a good animatable avatar automatically, given only a 3D static triangle mesh of the head. An automatic mechanism is devised for constructing multi‐layer animatable facial avatars for unseen faces. We evaluate our technique with a variety of models, and give a quantitative analysis of the constructed results. We also designed and conducted a user study for evaluating the perceived quality of the generated expressive animations. The results demonstrate that our method is an appropriate tool for naïve users to customize their personal 3D avatars. Copyright © 2010 John Wiley & Sons, Ltd.

We introduce a novel video stylisation framework based on decomposing the video volume into 3D Voronoi cells. Colour samples are taken for each cell in a video, leading to an efficient and sparse video representation. Based on the same representation, our framework affords a wide variety of artistic rendering styles. We present two families of such styles for reconstructing stylised video frames: (1) using neighbouring Voronoi cells, and (2) a derived per-frame Delaunay-like triangulation. Our framework provides a flexible foundation for automatic video stylisation that is artistically expressive and temporally coherent.

We present a subdivision framework that adds extraordinary vertices to NURBS of arbitrarily high degree. The surfaces can represent any odd degree NURBS patch exactly. Our rules handle non-uniform knot vectors, and are not restricted to midpoint knot insertion. In the absence of multiple knots at extraordinary points, the limit surfaces have bounded curvature.

Abstract We present a method for tuning primal stationary subdivision schemes to give the best possible behaviour near extraordinary vertices with respect to curvature variation. Current schemes lead to a limit surface around extraordinary vertices for which the Gaussian curvature diverges, as demonstrated by Karčiauskas et al. [ KPR04 ]. Even when coefficients are chosen such that the subsubdominant eigenvalues, μ , equal the square of the subdominant eigenvalue, λ , of the subdivision matrix [ DS78 ] there is still variation in the curvature of the subdivision surface around the extraordinary vertex as shown in recent work by Peters and Reif [ PR04 ] illustrated by Karčiauskas et al. [ KPR04 ]. In our tuning method we optimise within the space of subdivision schemes with bounded curvature to minimise this variation in curvature around the extraordinary vertex. To demonstrate our method we present results for the Catmull‐Clark [ CC78 ], 4‐8 [ Vel01 , VZ01 ] and 4‐3 [ PS03 ] subdivision schemes. We compare our results to previous work on the tuning of these schemes and show that the coefficients derived with this method give a significantly smaller curvature variation around extraordinary vertices. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling, I.3.6 [Computer Graphics]: Methodology and Techniques

Abstract Linear interpolation is the standard image blending method used in image compositing. By averaging in the dynamic range, it reduces contrast and visibly degrades the quality of composite imagery. We demonstrate how to correct linear interpolation to resolve this longstanding problem. To provide visually meaningful, high level control over the compositing process, we introduce three novel image blending operators that are designed to preserve key visual characteristics of their inputs. Our contrast preserving method applies a linear color mapping to recover the contrast lost due to linear interpolation. Our salience preserving method retains the most informative regions of the input images by balancing their relative opacity with their relative saliency. Our color preserving method extends homomorphic image processing by establishing an isomorphism between the image colors and the real numbers, allowing any mathematical operation defined on real numbers to be applied to colors without losing its algebraic properties or mapping colors out of gamut. These approaches to image blending have artistic uses in image editing and video production as well as technical applications such as image morphing and mipmapping. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation

We study the support of subdivision schemes: that is, the region of the subdivision surface that is affected by the displacement of a single control point. Our main results cover the regular case, where the mesh induces a regular Euclidean tesselation of the local parameter space. If n is the ratio of similarity between the tesselations at steps k and k − 1 of the refinement, we show that n determines the extent of this region and largely determines whether its boundary is polygonal or fractal. In particular if n = 2 (or n2 = 2 because we can always take double steps) the support is a convex polygon whose vertices can easily be determined. In other cases, whether the boundary of the support is fractal or not depends on whether there are sufficient points with non-zero coefficients in the edges of the convex hull of the mask. If there are enough points on every such edge, the support is again a convex polygon. If some edges have enough points and others do not, the boundary can consist of a fractal assembly of an unbounded number of line segments.

Abstract Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free‐form curve to define the profile of the blend region between implicit primitives. The use of a free‐form implicit curve, controlled point‐by‐point in the Euclidean user space, allows us to group boolean composition operators with sharp transitions or smooth free‐form transitions in a single modeling metaphor. This idea is generalized for the creation, sculpting and manipulation of volume objects, while providing the user with simplicity, controllability and freedom in implicit modeling. ACM CSS: I.3.5 Computational Gemoetry and Object Modeling—Curve, surface, solid, and object representations

We present a data structure for three-dimensional fields C/sup 1/ continuous in the modelling space. Regular grids storing the field values discretely are combined with a triquadratic approximation filter to define volume objects. This association of a grid and an approximation/interpolation filter allows the field to be defined by a C/sup 1/ continuous real function and the surface to be directly visualised from its own equation. We show how accurate and high quality interactive visualisation is obtained during the modelling process, and we explain why the visualisation is faithful to the object definition. We also describe, as an example of application of our data structure, how advanced Boolean operators realised with soft or "functionally controlled" transitions are performed under the influence of an interactive modelling tool.

We describe a method for efficient calculation of coefficients for subdivision schemes. We work on the unit sphere and we express the z-coordinate of all the existing points as power series in the variable cos /spl theta/. Any linear combination of them is also a power series in cos /spl theta/ and, by solving a linear system, we determine the linear combination that will give the smoothest interpolation of the sphere at a particular point.

Abstract This paper describes a simulation of attention behaviour aimed at computer‐animated characters. Attention is the focusing of a person's perception on a particular object. This is useful for computer animation as it determines which objects the character is aware of: information that can be used in the simulation of the character's behaviour in order to automatically animate the character. The simulation of attention also determines where the character is looking and so is used to produce gaze behaviour. Copyright © 2002 John Wiley & Sons, Ltd.

We present a simple method of interactive texture editing that utilizes self-similarity to replicate intended operations globally over an image. Inspired by the recent successes of hierarchical approaches to texture synthesis, this method also uses multi-scale neighborhoods to assess the similarity of pixels within a texture. However, neighborhood matching is not employed to generate new instances of a texture. We instead locate similar neighborhoods for the purpose of replicating editing operations on the original texture itself, thereby creating a fundamentally new texture. This general approach is applied to texture painting, cloning and warping. These global operations are performed interactively, most often directed with just a single mouse movement.

Free-Form Deformation (FFD) is a versatile and efficient modeling technique which transforms an object by warping the surrounding space. The conventional user-interface is a lattice of movable control points but this tends to be cumbersome and counterintuitive. Directly Manipulated Free-Form Deformation (DMFFD) allows the user to drag object points directly and has proven useful in an interactive sculpting context. A serious shortcoming of both FFD and DMFFD is that some deformations cause self-intersection of the object. This is unrealistic and compromises the object's validity and suitability for later use. An in-built self-intersection test is thus required for FFD and its extensions to be truly robust In this paper, we present the following novel results set of theoretical conditions for preventing self-intersection by ensuring the injectivity (one-to-one mapping) of FFD, an exact. (necessary and sufficient) injectivity test which is accurate but computationally costly, an efficient but approximate injectivity test which is a sufficient condition only, and a new form of DMFFD which acts by composing many small injective deformations. The latter expands the range of possible deformations without sacrificing the speed of the approximate test.

We present an image compression scheme that is error resilient and offers lossless decompression in the absence of channel noise. Attempts are made to detect transmission errors and data found to be in error is discarded so as not to pollute the decompressed output. This is achieved while still maintaining a level of compression that is competitive with lossless image compression standards.

Nearest-neighbor, linear, and various cubic interpolation functions are frequently used in image resampling. Quadratic functions have been disregarded largely because they have been thought to introduce phase distortions. This is shown not to be the case, and a family of quadratic functions is derived. The interpolating member of this family has visual quality close to that of the Catmull-Rom cubic, yet requires only 60% of the computation time.