Artist-drawn sketches only loosely conform to analytical models of perspective projection; the deviation of human-drawn perspective from analytical perspective models is persistent and well documented, but has yet to be algorithmically replicated. We encode this deviation between human and analytic perspectives as a continuous function in 3D space and develop a method to learn it. We seek deviation functions that (i) mimic artist deviation on our training data; (ii) generalize to other shapes; (iii) are consistent across different views of the same shape; and (iv) produce outputs that appear human-drawn. The natural data for learning this deviation is pairs of artist sketches of 3D shapes and best-matching analytical camera views of the same shapes. However, a core challenge in learning perspective deviation is the heterogeneity of human drawing choices, combined with relative data paucity (the datasets we rely on have only a few dozen training pairs). We sidestep this challenge by learning perspective deviation from an individual pair of an artist sketch of a 3D shape and the contours of the same shape rendered from a best-matching analytical camera view. We first match contours of the depicted shape to artist strokes, then learn a spatially continuous local perspective deviation function that modifies the camera perspective projecting the contours to their corresponding strokes. This function retains key geometric properties that artists strive to preserve when depicting 3D content, thus satisfying (i) and (iv) above. We generalize our method to alternative shapes and views (ii,iii) via a self-augmentation approach that algorithmically generates training data for nearby views, and enforces spatial smoothness and consistency across all views. We compare our results to potential alternatives, demonstrating the superiority of the proposed approach. Code and models will be released upon acceptance.

Compressed representations of 3D shapes that are compact, accurate, and can be processed efficiently directly in compressed form, are extremely useful for digital media applications. Recent approaches in this space focus on learned implicit or parametric representations. While implicits are well suited for tasks such as in-out queries, they lack natural 2D parameterization, complicating tasks such as texture or normal mapping. Conversely, parametric representations support the latter tasks but are ill-suited for occupancy queries. We propose a novel learned alternative to these approaches, based on intersections of localized explicit , or height-field , surfaces. Since explicits can be trivially expressed both implicitly and parametrically, NESI directly supports a wider range of processing operations than implicit alternatives, including occupancy queries and parametric access. We represent input shapes using a collection of differently oriented height-field bounded half-spaces combined using volumetric Boolean intersections. We first tightly bound each input using a pair of oppositely oriented height-fields, forming a Double Height-Field (DHF) Hull . We refine this hull by intersecting it with additional localized height-fields (HFs) that capture surface regions in its interior. We minimize the number of HFs necessary to accurately capture each input and compactly encode both the DHF hull and the local HFs as neural functions defined over subdomains of \(\mathbb {R}^2\) . This reduced dimensionality encoding delivers high-quality compact approximations. Given similar parameter count, or storage capacity, NESI significantly reduces approximation error compared to the state-of-the-art, especially at lower parameter counts.

Abstract Artist generated clip‐art images typically consist of a small number of distinct, uniformly colored regions with clear boundaries. Legacy artist created images are often stored in low‐resolution (100x100px or less) anti‐aliased raster form. Compared to anti‐aliasing free rasterization, anti‐aliasing blurs inter‐region boundaries and obscures the artist's intended region topology and color palette; at the same time, it better preserves subpixel details. Recovering the underlying artist‐intended images from their low‐resolution anti‐aliased rasterizations can facilitate resolution independent rendering, lossless vectorization, and other image processing applications. Unfortunately, while human observers can mentally deblur these low‐resolution images and reconstruct region topology, color and subpixel details, existing algorithms applicable to this task fail to produce outputs consistent with human expectations when presented with such images. We recover these viewer perceived blur‐free images at subpixel resolution, producing outputs where each input pixel is replaced by four corresponding (sub)pixels. Performing this task requires computing the size of the output image color palette, generating the palette itself, and associating each pixel in the output with one of the colors in the palette. We obtain these desired output components by leveraging a combination of perceptual and domain priors, and real world data. We use readily available data to train a network that predicts, for each anti‐aliased image, a low‐blur approximation of the blur‐free double‐resolution outputs we seek. The images obtained at this stage are perceptually closer to the desired outputs but typically still have hundreds of redundant differently colored regions with fuzzy boundaries. We convert these low‐blur intermediate images into blur‐free outputs consistent with viewer expectations using a discrete partitioning procedure guided by the characteristic properties of clip‐art images, observations about the antialiasing process, and human perception of anti‐aliased clip‐art. This step dramatically reduces the size of the output color palettes, and the region counts bringing them in line with viewer expectations and enabling the image processing applications we target. We demonstrate the utility of our method by using our outputs for a number of image processing tasks, and validate it via extensive comparisons to prior art. In our comparative study, participants preferred our deblurred outputs over those produced by the best‐performing alternative by a ratio of 75 to 8.5.

3-axis milling enables cheap and precise fabrication of target objects from precut slabs of materials such as wood or stone. However, the space of directly millable shapes is limited since a 3-axis mill can only carve a height-field (HF) surface during each milling and their size is bounded by the slab dimensions, one of which, the height , is typically significantly smaller than the other two for many typical materials. Extending 3-axis milling of precut slabs to general arbitrarily-sized shapes requires decomposing them into bounded-height 3-axis millable parts, or slices , which can be individually milled and then assembled to form the target object. We present DHFSlicer , a novel decomposition method that satisfies the above constraints and significantly reduces both milling time and material waste compared to alternative approaches. We satisfy the fabrication constraints by partitioning target objects into double height-field (DHF) slices, which can be fabricated using two milling passes: the HF surface accessible from one side is milled first, the slice is then flipped using appropriate fixtures, and then the second, remaining, HF surface is milled. DHFSlicer uses an efficient coarse-to-fine decomposition process: It first partitions the inputs into maximally coarse blocks that satisfy a local DHF criterion with respect to per-block milling axes, and then cuts each block into well-sized DHF slices. It minimizes milling time and material waste by keeping the slice count small, and maximizing slice height. We validate our method by embedding it within an end-to-end DHF milling pipeline and fabricating objects from slabs of foam, wood, and MDF; demonstrate that using the obtained slices reduces milling time and material waste by 42% on average compared to existing automatic alternatives; and highlight the benefits of DHFSlicer via extensive ablation studies.