DOCSLIB.ORG

Learning Perspective Undistortion of Portraits

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Learning Perspective Undistortion of Portraits Learning Perspective Undistortion of Portraits Yajie Zhao1,*, Zeng Huang1,2,*, Tianye Li1,2, Weikai Chen1, Chloe LeGendre1,2, Xinglei Ren1, Jun Xing1, Ari Shapiro1, and Hao Li1,2,3 1USC Institute for Creative Technologies 2University of Southern California 3Pinscreen Beam Splitter Fixed Camera Sliding Camera (a) Capture Setting (b) Input image (c) Undistorted image (d) Reference (e) Input image (f) Undistorted image (g) Reference Figure 1: We propose a learning-based method to remove perspective distortion from portraits. For a subject with two different facial expressions, we show input photos (b) (e), our undistortion results (c) (f), and reference images (d) (g) captured simultaneously using a beam splitter rig (a). Our approach handles even extreme perspective distortions. Abstract 1. Introduction Perspective distortion artifacts are often observed in Near-range portrait photographs often contain perspec- portrait photographs, in part due to the popularity of the tive distortion artifacts that bias human perception and “selfie” image captured at a near-range distance. The challenge both facial recognition and reconstruction tech- inset images, where a person is photographed from dis- niques. We present the first deep learning based approach tances of 160cm and 25cm, demonstrate these artifacts. to remove such artifacts from unconstrained portraits. In When the object-to- contrast to the previous state-of-the-art approach [25], our camera distance is method handles even portraits with extreme perspective dis- comparable to the size of tortion, as we avoid the inaccurate and error-prone step of a human head, as in the first fitting a 3D face model. Instead, we predict a distor- 25cm distance example, tion correction flow map that encodes a per-pixel displace- there is a large propor- ment that removes distortion artifacts when applied to the tional difference between arXiv:1905.07515v1 [cs.CV] 18 May 2019 input image. Our method also automatically infers missing the camera-to-nose dis- facial features, i.e. occluded ears caused by strong perspec- tance and camera-to-ear tive distortion, with coherent details. We demonstrate that @160CM @25CM distance. This difference our approach significantly outperforms the previous state- creates a face with unusual proportions, with the nose and of-the-art [25] both qualitatively and quantitatively, partic- eyes appearing larger and the ears vanishing all together ularly for portraits with extreme perspective distortion or [61]. facial expressions. We further show that our technique ben- Perspective distortion in portraits not only influences the efits a number of fundamental tasks, significantly improving way humans perceive one another [10], but also greatly im- the accuracy of both face recognition and 3D reconstruc- pairs a number of computer vision-based tasks, such as face tion and enables a novel camera calibration technique from verification and landmark detection. Prior research [41, 42] a single portrait. Moreover, we also build the first perspec- has demonstrated that face recognition is strongly compro- tive portrait database with a large diversity in identities, mised by the perspective distortion of facial features. Ad- expression and poses. ditionally, 3D face reconstruction from such portraits is 1 highly inaccurate, as geometry fitting starts from biased fa- missing facial features like ears or the rim of the face. We cial landmarks and distorted textures. show that our approach significantly outperforms Fried et Correcting perspective distortion in portrait photography al. [25] both qualitatively and quantitatively for a synthetic is a largely unstudied topic. Recently, Fried et al. [25] in- dataset, constrained portraits, and unconstrained portraits vestigated a related problem, aiming to manipulate the rel- from the Internet. We also show that our proposed face ative pose and distance between a camera and a subject in a undistortion technique, when applied as a pre-processing given portrait. Towards this goal, they fit a full perspective step, improves a wide range of fundamental tasks in com- camera and parametric 3D head model to the input image puter vision and computer graphics, including face recogni- and performed 2D warping according to the desired change tion/verification, landmark detection on near-range portraits in 3D. However, the technique relied on a potentially inac- (such as head mounted cameras in visual effects), and 3D curate 3D reconstruction from facial landmarks biased by face model reconstruction, which can help 3D avatar cre- perspective distortion. Furthermore, if the 3D face model ation and the generation of 3D photos (Section 6.3). Ad- fitting step failed, as it could for extreme perspective distor- ditionally, our novel camera distance prediction provides tion or dramatic facial expressions, so would their broader accurate camera calibration from a single portrait. pose manipulation method. In contrast, our approach does Our main contributions can be summarized as follows: not rely on model fitting from distorted inputs and thus can • The first deep learning based method to automatically handle even these challenging inputs. Our GAN-based syn- remove perspective distortion from an unconstrained thesis approach also enables high-fidelity inference of any near-range portrait, benefiting a wide range of funda- occluded features, not considered by Fried et al. [25]. mental tasks in computer vision and graphics. In our approach, we propose a cascaded network that maps a near-range portrait with perspective distortion to its • A novel and accurate camera calibration approach that distortion-free counterpart at a canonical distance of 1:6m only requires a single near-range portrait as input. (although any distance between 1:4m ∼ 2m could be used as the target distance for good portraits). Our cascaded net- • A new perspective portrait database for face undistor- work includes a distortion correction flow network and a tion with a wide range of subject identities, head poses, completion network. Our distortion correction flow method camera distances, and lighting conditions. encodes a per-pixel displacement, maintaining the origi- nal image’s resolution and its high frequency details in the 2. Related Work output. However, as near-range portraits often suffer from Face Modeling. We refer the reader to [46] for a com- significant perspective occlusions, flowing individual pixels prehensive overview and introduction to the modeling of often does not yield a complete final image. Thus, the com- digital faces. With advances in 3D scanning and sens- pletion network inpaints any missing features. A final tex- ing technologies, sophisticated laboratory capture systems ture blending step combines the face from the completion [6,7,9, 23, 26, 40, 44, 62] have been developed for high- network and the warped output from the distortion correc- quality face reconstruction. However, 3D face geometry tion network. As the possible range of per-pixel flow values reconstruction from a single unconstrained image remains vary by camera distance, we first train a camera distance challenging. The seminal work of Blanz and Vetter [8] pro- prediction network, and feed this prediction along with the posed a PCA-based morphable model, which laid the foun- input portrait to the distortion correction network. dation for modern image-based 3D face modeling and in- Training our proposed networks requires a large corpus spired numerous extensions including face modeling from of paired portraits with and without perspective distortion. internet pictures [35], multi-view stereo [3], and reconstruc- However, to the best of our knowledge, no previously ex- tion based on shading cues [36]. To better capture a vari- isting dataset is suited for this task. As such, we construct ety of identities and facial expressions, the multi-linear face the first portrait dataset rendered from 3D head models with models [60] and the FACS-based blendshapes [12] were large variations in camera distance, head pose, subject iden- later proposed. When reconstructing a 3D face from im- tity, and illumination. To visually and numerically evalu- ages, sparse 2D facial landmarks [20, 21, 52, 65] are widely ate the effectiveness of our approach on real portrait pho- used for a robust initialization. Shape regressions have tographs, we also design a beam-splitter photography sys- been exploited in the state-of-the-art landmark detection ap- tem (see Teaser) to capture portrait pairs of real subjects proaches [13, 34, 48] to achieve impressive accuracy. simultaneously on the same optical axis, eliminating differ- Due to the low dimensionality and effectiveness of mor- ences in poses, expressions and lighting conditions. phable models in representing facial geometry, there have Experimental results demonstrate that our approach re- been significant recent advances in single-view face recon- moves a wide range of perspective distortion artifacts (e.g., struction [56, 49, 38, 55, 30]. However, for near-range por- increased nose size, squeezed face, etc), and even restores trait photos, the perspective distortion of facial features may lead to erroneous reconstructions even when using the state- using vanishing points from a single scene photos with hori- of-the-art techniques. Therefore, portrait perspective undis- zontal lines. To the best of our knowledge, our method is the tortion must be considered as a part of a pipeline for accu- first to estimate camera parameters from a single portrait. rately modeling facial geometry. 3. Overview
Load more

Recommended publications
  • Breaking Down the “Cosine Fourth Power Law”
    Breaking Down The “Cosine Fourth Power Law” By Ronian Siew, inopticalsolutions.com Why are the corners of the field of view in the image captured by a camera lens usually darker than the center? For one thing, camera lenses by design often introduce “vignetting” into the image, which is the deliberate clipping of rays at the corners of the field of view in order to cut away excessive lens aberrations. But, it is also known that corner areas in an image can get dark even without vignetting, due in part to the so-called “cosine fourth power law.” 1 According to this “law,” when a lens projects the image of a uniform source onto a screen, in the absence of vignetting, the illumination flux density (i.e., the optical power per unit area) across the screen from the center to the edge varies according to the fourth power of the cosine of the angle between the optic axis and the oblique ray striking the screen. Actually, optical designers know this “law” does not apply generally to all lens conditions.2 – 10 Fundamental principles of optical radiative flux transfer in lens systems allow one to tune the illumination distribution across the image by varying lens design characteristics. In this article, we take a tour into the fascinating physics governing the illumination of images in lens systems. Relative Illumination In Lens Systems In lens design, one characterizes the illumination distribution across the screen where the image resides in terms of a quantity known as the lens’ relative illumination — the ratio of the irradiance (i.e., the power per unit area) at any off-axis position of the image to the irradiance at the center of the image.
    [Show full text]
  • Estimation and Correction of the Distortion in Forensic Image Due to Rotation of the Photo Camera
    Master Thesis Electrical Engineering February 2018 Master Thesis Electrical Engineering with emphasis on Signal Processing February 2018 Estimation and Correction of the Distortion in Forensic Image due to Rotation of the Photo Camera Sathwika Bavikadi Venkata Bharath Botta Department of Applied Signal Processing Blekinge Institute of Technology SE–371 79 Karlskrona, Sweden This thesis is submitted to the Department of Applied Signal Processing at Blekinge Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering with Emphasis on Signal Processing. Contact Information: Author(s): Sathwika Bavikadi E-mail: [email protected] Venkata Bharath Botta E-mail: [email protected] Supervisor: Irina Gertsovich University Examiner: Dr. Sven Johansson Department of Applied Signal Processing Internet : www.bth.se Blekinge Institute of Technology Phone : +46 455 38 50 00 SE–371 79 Karlskrona, Sweden Fax : +46 455 38 50 57 Abstract Images, unlike text, represent an effective and natural communica- tion media for humans, due to their immediacy and the easy way to understand the image content. Shape recognition and pattern recog- nition are one of the most important tasks in the image processing. Crime scene photographs should always be in focus and there should be always be a ruler be present, this will allow the investigators the ability to resize the image to accurately reconstruct the scene. There- fore, the camera must be on a grounded platform such as tripod. Due to the rotation of the camera around the camera center there exist the distortion in the image which must be minimized.
    [Show full text]
  • Effects on Map Production of Distortions in Photogrammetric Systems J
    EFFECTS ON MAP PRODUCTION OF DISTORTIONS IN PHOTOGRAMMETRIC SYSTEMS J. V. Sharp and H. H. Hayes, Bausch and Lomb Opt. Co. I. INTRODUCTION HIS report concerns the results of nearly two years of investigation of T the problem of correlation of known distortions in photogrammetric sys­ tems of mapping with observed effects in map production. To begin with, dis­ tortion is defined as the displacement of a point from its true position in any plane image formed in a photogrammetric system. By photogrammetric systems of mapping is meant every major type (1) of photogrammetric instruments. The type of distortions investigated are of a magnitude which is considered by many photogrammetrists to be negligible, but unfortunately in their combined effects this is not always true. To buyers of finished maps, you need not be alarmed by open discussion of these effects of distortion on photogrammetric systems for producing maps. The effect of these distortions does not limit the accuracy of the map you buy; but rather it restricts those who use photogrammetric systems to make maps to limits established by experience. Thus the users are limited to proper choice of flying heights for aerial photography and control of other related factors (2) in producing a map of the accuracy you specify. You, the buyers of maps are safe behind your contract specifications. The real difference that distortions cause is the final cost of the map to you, which is often established by competi­ tive bidding. II. PROBLEM In examining the problem of correlating photogrammetric instruments with their resultant effects on map production, it is natural to ask how large these distortions are, whose effects are being considered.
    [Show full text]
  • Model-Free Lens Distortion Correction Based on Phase Analysis of Fringe-Patterns
    sensors Article Model-Free Lens Distortion Correction Based on Phase Analysis of Fringe-Patterns Jiawen Weng 1,†, Weishuai Zhou 2,†, Simin Ma 1, Pan Qi 3 and Jingang Zhong 2,4,* 1 Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China; [email protected] (J.W.); [email protected] (S.M.) 2 Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China; [email protected] 3 Department of Electronics Engineering, Guangdong Communication Polytechnic, Guangzhou 510650, China; [email protected] 4 Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Guangzhou 510650, China * Correspondence: [email protected] † The authors contributed equally to this work. Abstract: The existing lens correction methods deal with the distortion correction by one or more specific image distortion models. However, distortion determination may fail when an unsuitable model is used. So, methods based on the distortion model would have some drawbacks. A model- free lens distortion correction based on the phase analysis of fringe-patterns is proposed in this paper. Firstly, the mathematical relationship of the distortion displacement and the modulated phase of the sinusoidal fringe-pattern are established in theory. By the phase demodulation analysis of the fringe-pattern, the distortion displacement map can be determined point by point for the whole distorted image. So, the image correction is achieved according to the distortion displacement map by a model-free approach. Furthermore, the distortion center, which is important in obtaining an optimal result, is measured by the instantaneous frequency distribution according to the character of distortion automatically. Numerical simulation and experiments performed by a wide-angle lens are carried out to validate the method.
    [Show full text]
  • Optics II: Practical Photographic Lenses CS 178, Spring 2013
    Optics II: practical photographic lenses CS 178, Spring 2013 Begun 4/11/13, finished 4/16/13. Marc Levoy Computer Science Department Stanford University Outline ✦ why study lenses? ✦ thin lenses • graphical constructions, algebraic formulae ✦ thick lenses • center of perspective, 3D perspective transformations ✦ depth of field ✦ aberrations & distortion ✦ vignetting, glare, and other lens artifacts ✦ diffraction and lens quality ✦ special lenses • 2 telephoto, zoom © Marc Levoy Lens aberrations ✦ chromatic aberrations ✦ Seidel aberrations, a.k.a. 3rd order aberrations • arise because we use spherical lenses instead of hyperbolic • can be modeled by adding 3rd order terms to Taylor series ⎛ φ 3 φ 5 φ 7 ⎞ sin φ ≈ φ − + − + ... ⎝⎜ 3! 5! 7! ⎠⎟ • oblique aberrations • field curvature • distortion 3 © Marc Levoy Dispersion (wikipedia) ✦ index of refraction varies with wavelength • higher dispersion means more variation • amount of variation depends on material • index is typically higher for blue than red • so blue light bends more 4 © Marc Levoy red and blue have Chromatic aberration the same focal length (wikipedia) ✦ dispersion causes focal length to vary with wavelength • for convex lens, blue focal length is shorter ✦ correct using achromatic doublet • strong positive lens + weak negative lens = weak positive compound lens • by adjusting dispersions, can correct at two wavelengths 5 © Marc Levoy The chromatic aberrations (Smith) ✦ longitudinal (axial) chromatic aberration • different colors focus at different depths • appears everywhere
    [Show full text]
  • Distortion-Free Wide-Angle Portraits on Camera Phones
    Distortion-Free Wide-Angle Portraits on Camera Phones YICHANG SHIH, WEI-SHENG LAI, and CHIA-KAI LIANG, Google (a) A wide-angle photo with distortions on subjects’ faces. (b) Distortion-free photo by our method. Fig. 1. (a) A group selfie taken by a wide-angle 97° field-of-view phone camera. The perspective projection renders unnatural look to faces on the periphery: they are stretched, twisted, and squished. (b) Our algorithm restores all the distorted face shapes and keeps the background unaffected. Photographers take wide-angle shots to enjoy expanding views, group por- ACM Reference Format: traits that never miss anyone, or composite subjects with spectacular scenery background. In spite of the rapid proliferation of wide-angle cameras on YiChang Shih, Wei-Sheng Lai, and Chia-Kai Liang. 2019. Distortion-Free mobile phones, a wider field-of-view (FOV) introduces a stronger perspec- Wide-Angle Portraits on Camera Phones. ACM Trans. Graph. 38, 4, Article 61 tive distortion. Most notably, faces are stretched, squished, and skewed, to (July 2019), 12 pages. https://doi.org/10.1145/3306346.3322948 look vastly different from real-life. Correcting such distortions requires pro- fessional editing skills, as trivial manipulations can introduce other kinds of distortions. This paper introduces a new algorithm to undistort faces 1 INTRODUCTION without affecting other parts of the photo. Given a portrait as an input,we formulate an optimization problem to create a content-aware warping mesh Empowered with extra peripheral vi- FOV=97° which locally adapts to the stereographic projection on facial regions, and sion to “see”, a wide-angle lens is FOV=76° seamlessly evolves to the perspective projection over the background.
    [Show full text]
  • On Photogrammetric Distortion 763
    HORST SCHOLER lena Optics lena GMBH, German Democratic Republic On Photogram metric Distortion Compensation for model deformations is afforded by electrical- analogue computers both for planimetry and elevation, allowing one to generate mutually independent correction surfaces in both directions. INTRODUCTION DISTORTION IN OPTICAL IMAGING SYSTEMS ITH THE ADVANCE of photogrammetric Normally, image formation by an optical­ W methods with respect to measuring ac­ photographical system is, to a first approxi­ curacy, systematic model deformations are mation, based on the mathematical­ claiming closer attention. In relevant publi­ geometrical model ofperspective projection. cations, frequent use is made of the word In any physical implementation of optical distortion as a component of various terms imaging by glass elements of(mostly) spheri­ such as asymmetrical distortion, tangential cal curvature, deviations from this model will distortion, etc. In photogrammetric instru- occur due to the laws of geometric optics. ABSTRACT: The term "distortion" is precisely defined as the symmet­ rical dislocation ofimage points between the mathematical model of perspective projection and the physical image formation model. On this physical distortion, which is always rotation-symmetrical, is superposed a summation ofunavoidable tolerances in the manufac­ ture of optical systems, for which the term "deformation" is intro­ duced. Further considerations deal with external influences on photogrammetric photography and lead to the conclusion that at the present state ofknowledge no definite causes can be established for image point dislocations in photographic image formation. Based on the assumption that model deformations are caused by imperfections ofthe photograph's geometry, it is advantageous to compensate those imperfections by correction surfaces generated analytically or by analogue instrumental techniques from discrepancies at known con­ trol points.
    [Show full text]
  • The Precise Evaluation of Lens Distortion*
    The Precise Evaluation of Lens Distortion* FRA CIS E. WASHER, National Bureau of Standards, Washington, D. C. ABSTRACT: Four methods of radial distortion measurement are described. Com­ parison of results obtained on the same lens using each of the four methods is used to locate systematic errors and to evaluate the reliability of each method. Several sources of error are discussed. It is concluded that a precision of ±2 microns can be achieved using anyone of the four methods provided adequate attention is given to the reduction of all potential errors to negligible proportions: that is, the PE 8 of D{3 does not exceed 2 microns where D{3 is the value of distor­ tion obtained at angle fJ and PE 8 is the probable error of a single determination. 1. INTRODUCTION which is used to considerable extent In Europe. HE measurement of radial distortion in T the focal-plane of photographic objec­ Because of the diversity of methods used in tives has been the subject of intensive study evaluation of distortion, it seemed worth­ since the advent of mapping from aerial while to investigate the results of measure­ photographs. This particular aberration is of ments made in a single laboratory on a single prime interest to photogrammetrists as its lens by a variety of methods, to determine magnitude determines the accuracy with whether or not the values so obtained varied which the final negative maintains the correct appreciably \\"ith the method. This has been relationships among the array of point images done using four different methods and a com­ making up the photography of the cor­ parison of the results is reported in this paper.
    [Show full text]
  • Vignette and Exposure Calibration and Compensation
    Vignette and Exposure Calibration and Compensation Dan B Goldman and Jiun-Hung Chen University of Washington Figure 1 On the left, a panoramic sequence of images showing vignetting artifacts. Note the change in brightness at the edge of each image. Although the effect is visually subtle, this brightness change corresponds to a 20% drop in image intensity from the center to the corner of each image. On the right, the same sequence after vignetting is removed. Abstract stereo correlation and optical flow. Yet despite its occur- rence in essentially all photographed images, and its detri- We discuss calibration and removal of “vignetting” (ra- mental effect on these algorithms and systems, relatively dial falloff) and exposure (gain) variations from sequences little attention has been paid to calibrating and correcting of images. Unique solutions for vignetting, exposure and vignette artifacts. scene radiances are possible when the response curve is As we demonstrate, vignetting can be corrected easily known. When the response curve is unknown, an exponen- using sequences of natural images without special calibra- tial ambiguity prevents us from recovering these parameters tion objects or lighting. Our approach can be used even uniquely. However, the vignetting and exposure variations for existing panoramic image sequences in which nothing is can nonetheless be removed from the images without resolv- known about the camera. Figure 1 shows a series of aligned ing this ambiguity. Applications include panoramic image images, exhibiting noticeable brightness change along the mosaics, photometry for material reconstruction, image- boundaries of the images, even though the exposure of each based rendering, and preprocessing for correlation-based image is identical.
    [Show full text]
  • Fisheye Distortion Rectification from Deep Straight Lines
    1 Fisheye Distortion Rectification from Deep Straight Lines Zhu-Cun Xue, Nan Xue, Gui-Song Xia Abstract—This paper presents a novel line-aware rectification network (LaRecNet) to address the problem of fisheye distortion rectification based on the classical observation that straight lines in 3D space should be still straight in image planes. Specifically, the proposed LaRecNet contains three sequential modules to (1) learn the distorted straight lines from fisheye images; (2) estimate the distortion parameters from the learned heatmaps and the image appearance; and (3) rectify the input images via a proposed differentiable rectification layer. To better train and evaluate the proposed model, we create a synthetic line-rich fisheye (SLF) dataset that contains the distortion parameters and well-annotated distorted straight lines of fisheye images. The proposed method enables us to simultaneously calibrate the geometric distortion parameters and rectify fisheye images. Extensive experiments demonstrate that our model achieves state-of-the-art performance in terms of both geometric accuracy and image quality on several evaluation metrics. In particular, the images rectified by LaRecNet achieve an average reprojection error of 0.33 pixels on the SLF dataset and produce the highest peak signal-to-noise ratio (PSNR) and structure similarity index (SSIM) compared with the groundtruth. Index Terms—Fisheye Distortion Rectification, Fisheye Camera Calibration, Deep Learning, Straight Line Constraint F 1 INTRODUCTION Fisheye cameras enable us to capture images with an Straighten the Distorted Lines ultrawide field of view (FoV) and have the potential to ben- efit many machine vision tasks, such as structure from mo- LaRecNet tion (SfM), simultaneous localization and mapping (SLAM) and autonomous driving, by perceiving a well-conditioned scene coverage with fewer images than would otherwise be required.
    [Show full text]
  • An Exact Formula for Calculating Inverse Radial Lens Distortions
    sensors Article An Exact Formula for Calculating Inverse Radial Lens Distortions Pierre Drap *,† and Julien Lefèvre † Aix-Marseille Université, CNRS, ENSAM, Université De Toulon, LSIS UMR 7296, Domaine Universitaire de Saint-Jérôme, Bâtiment Polytech, Avenue Escadrille Normandie-Niemen, Marseille 13397, France; [email protected] * Correspondence: [email protected]; Tel.: +33-4-91-82-85-20 † These authors contributed equally to this work. Academic Editor: Manuela Vieira Received: 4 March 2016; Accepted: 24 May 2016; Published: 1 June 2016 Abstract: This article presents a new approach to calculating the inverse of radial distortions. The method presented here provides a model of reverse radial distortion, currently modeled by a polynomial expression, that proposes another polynomial expression where the new coefficients are a function of the original ones. After describing the state of the art, the proposed method is developed. It is based on a formal calculus involving a power series used to deduce a recursive formula for the new coefficients. We present several implementations of this method and describe the experiments conducted to assess the validity of the new approach. Such an approach, non-iterative, using another polynomial expression, able to be deduced from the first one, can actually be interesting in terms of performance, reuse of existing software, or bridging between different existing software tools that do not consider distortion from the same point of view. Keywords: radial distortion; distortion correction; power series 1. Introduction Distortion is a physical phenomenon that in certain situations may greatly impact an image’s geometry without impairing quality nor reducing the information present in the image.
    [Show full text]
  • Correction of Geometric Perceptual Distortions in Pictures 1995
    Correction of Geometric Perceptual Distortions in Pictures Thesis by Denis N Zorin In Partial Fulllment of the Requirements for the Degree of Master of Science California Institute of Technology Pasadena California i Abstract We suggest an approach for correcting several typ es of p erceived geometric distortions in computer generated and photographic images The approach is based on a mathematical formalization of desirable prop erties of pictures Weprovide a review of p erception of pictures and identify p erceptually imp ortant geometric prop erties of images From a small set of simple assumptions we obtain p erceptually preferable pro jections of three dimensional space into the plane and show that these pro jections can b e decomp osed into a p er sp ective or parallel pro jection followed by a planar transformation The decomp osition is easily implemented and provides a convenient framework for further analysis of the image mapping Weprove that two p erceptually imp ortant prop erties are incompatible and cannot b e satised simultaneously It is imp ossible to construct a pro jection such that the images of all lines are straight and the images of all spheres are exact circles Perceptually preferable tradeos b etween these two typ es of distortions can dep end on the content of the picture We construct parametric families of pro jections with parameters representing the relative imp ortance of the p erceptual characteristics By adjusting the settings of the parameters we can minimize the overall distortion of the picture It turns
    [Show full text]