nips nips2013 nips2013-37 knowledge-graph by maker-knowledge-mining

37 nips-2013-Approximate Bayesian Image Interpretation using Generative Probabilistic Graphics Programs

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Author: Vikash Mansinghka, Tejas D. Kulkarni, Yura N. Perov, Josh Tenenbaum

Abstract: The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difﬁcult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple probabilistic graphics programs that deﬁne ﬂexible generative models and to automatically invert them to interpret real-world images. Generative probabilistic graphics programs (GPGP) consist of a stochastic scene generator, a renderer based on graphics software, a stochastic likelihood model linking the renderer’s output and the data, and latent variables that adjust the ﬁdelity of the renderer and the tolerance of the likelihood. Representations and algorithms from computer graphics are used as the deterministic backbone for highly approximate and stochastic generative models. This formulation combines probabilistic programming, computer graphics, and approximate Bayesian computation, and depends only on generalpurpose, automatic inference techniques. We describe two applications: reading sequences of degraded and adversarially obscured characters, and inferring 3D road models from vehicle-mounted camera images. Each of the probabilistic graphics programs we present relies on under 20 lines of probabilistic code, and yields accurate, approximately Bayesian inferences about real-world images. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Here we show that it is possible to write short, simple probabilistic graphics programs that deﬁne ﬂexible generative models and to automatically invert them to interpret real-world images. [sent-7, score-0.746]

2 Representations and algorithms from computer graphics are used as the deterministic backbone for highly approximate and stochastic generative models. [sent-9, score-0.594]

3 This formulation combines probabilistic programming, computer graphics, and approximate Bayesian computation, and depends only on generalpurpose, automatic inference techniques. [sent-10, score-0.305]

4 We describe two applications: reading sequences of degraded and adversarially obscured characters, and inferring 3D road models from vehicle-mounted camera images. [sent-11, score-0.416]

5 Each of the probabilistic graphics programs we present relies on under 20 lines of probabilistic code, and yields accurate, approximately Bayesian inferences about real-world images. [sent-12, score-0.746]

6 1 Introduction Computer vision has historically been formulated as the problem of producing symbolic descriptions of scenes from input images [10]. [sent-13, score-0.18]

7 This is usually done by building bottom-up processing pipelines that isolate the portions of the image associated with each scene element and extract features that signal its identity. [sent-14, score-0.449]

8 Many pattern recognition and learning techniques can then be used to build classiﬁers for individual scene elements, and sometimes to learn the features themselves [11, 7]. [sent-15, score-0.307]

9 Bottom-up pipelines that combine image processing and machine learning can identify written characters with high accuracy and recognize objects from large sets of possibilities. [sent-17, score-0.242]

10 Generative models for a range of image parsing tasks are also being explored [17, 4, 18, 22, 20]. [sent-21, score-0.175]

11 But like traditional bottom-up pipelines for vision, these approaches have relied on considerable problem-speciﬁc engineering, chieﬂy to design and/or learn custom inference strategies, such as MCMC proposals [18, 22] that incorporate bottom-up cues. [sent-28, score-0.258]

12 In this paper, we propose a novel formulation of image interpretation problems, called generative probabilstic graphics programming (GPGP). [sent-31, score-0.709]

13 Our probabilistic graphics programs are written in Venture, a probabilistic programming language descended from Church [6]. [sent-33, score-0.774]

14 Unlike typical generative models for scene parsing, inverting our probabilistic graphics programs requires no custom inference algorithm design. [sent-36, score-1.193]

15 Instead, we rely on the automatic Metropolis-Hastings (MH) transition operators provided by our probabilistic programming system. [sent-37, score-0.184]

16 The approximations and stochasticity in our renderer, scene generator and likelihood models serve to implement a variant of approximate Bayesian computation [19, 12]. [sent-38, score-0.531]

17 To the best of our knowledge, our GPGP framework is the ﬁrst real-world image interpretation formulation to combine all of the following elements: probabilistic programming, automatic inference, computer graphics, and approximate Bayesian computation; this constitutes our main contribution. [sent-40, score-0.356]

18 Our second contribution is to provide demonstrations of the efﬁcacy of this approach on two image interpretation problems: reading snippets of degraded and adversarially obscured alphanumeric characters, and inferring 3D road models from vehicle mounted cameras. [sent-41, score-0.577]

19 GPGP deﬁnes generative models for images by combining four components. [sent-44, score-0.166]

20 The ﬁrst is a stochastic scene generator written as probabilistic code that makes random choices for the location and conﬁguration of the main elements in the scene. [sent-45, score-0.529]

21 The second is an approximate renderer based on existing graphics software that maps a scene S and control variables X to an image IR = f (S, X). [sent-46, score-1.287]

22 The third is a stochastic likelihood model for image data ID that enables scoring of rendered scenes given the control variables. [sent-47, score-0.476]

23 The fourth is a set of latent variables X that control the ﬁdelity of the renderer and/or the tolerance in the stochastic likelihood model. [sent-48, score-0.597]

24 We ﬁrst give a general description of the generative model and inference algorithm induced by our probabilistic graphics programs; in later sections, we describe speciﬁc details for each application. [sent-51, score-0.748]

25 Let S = {Si } be a decomposition of the scene S into parts Si with independent priors P (Si ). [sent-52, score-0.271]

26 Each of our models shares a common template: a stochastic scene generator which samples possible scenes S according to their prior, latent variables X that control the ﬁdelity of the rendering and the tolerance of the model, an approximate render f (S, X) ! [sent-55, score-0.69]

27 IR based on existing graphics software, and a stochastic likelihood model P (ID |IR , X) that links observed rendered images. [sent-56, score-0.637]

28 A scene S ⇤ sampled from the scene generator according to ⇤ P (S) could be rendered onto a single image IR . [sent-57, score-0.916]

29 Instead of requiring exact matches, our formulation can broaden the renderer’s output ⇤ P (IR |S⇤) and the image likelihood P (ID |IR ) via the latent control variables X. [sent-59, score-0.264]

30 Our proposals modify single elements of the scene and control variables at a time, as follows: P (S) = Y P (Si ) 0 0 qi (Si , Si ) = P (Si ) P (X) = i Y P (Xj ) 0 0 qj (Xj , Xj ) = P (Xj ) j Now let K = |{Si }| + |{Xj }| be the total number of random variables in each execution. [sent-62, score-0.345]

31 If k corresponds to a scene variable i, then we propose from qi (Si , Si ), 0 0 0 0 0 so our overall proposal kernel q((S, X) ! [sent-67, score-0.271]

32 In both cases we re-render the scene IR = f (S 0 , X 0 ). [sent-70, score-0.271]

33 (S 0 , X 0 )) We implement our probabilistic graphics programs in the Venture probabilistic programming language. [sent-74, score-0.774]

34 The Metropolis-Hastings inference algorithm we use is provided by default in this system; no custom inference code is required. [sent-75, score-0.288]

35 ABC methods approximate Bayesian inference over complex generative processes by using an exogenous distance function to compare sampled outputs with observed data. [sent-77, score-0.267]

36 Our formulation incorporates a combination of these insights: rendered scenes are only approximately constrained to match the observed image, with the tightness of the match mediated by inference over factors such as the ﬁdelity of the rendering and the stochasticity in the likelihood. [sent-81, score-0.438]

37 3 Figure 2: Four input images from our CAPTCHA corpus, along with the ﬁnal results and convergence trajectory of typical inference runs. [sent-83, score-0.16]

38 Our probabilistic graphics program did not originally support rotation, which was needed for the AOL CAPTCHAs; adding it required only 1 additional line of probabilistic code. [sent-86, score-0.691]

39 We developed a probabilistic graphics program for reading short snippets of degraded text consisting of arbitrary digits and letters. [sent-89, score-0.787]

40 5 P (Si = x) = P (Si = y) = 0 otherwise 0 otherwise glyph id P (Si = g) = ( 1/G 0 glyph id 0  Si < ✓max otherwise Our renderer rasterizes each letter independently, applies a spatial blur to each image, composites the letters, and then blurs the result. [sent-92, score-1.24]

41 We also applied global blur to the original training image before applying the stochastic likelihood model on the blurred original and rendered images. [sent-93, score-0.588]

42 To assess the accuracy of our approach on adversarially obscured text, we developed a corpus consisting of over 40 images from widely used websites such as TurboTax, E-Trade, and AOL, plus additional challenging synthetic CAPTCHAs with high degrees of letter overlap and superimposed distractors. [sent-99, score-0.286]

43 Each source of text violates the underlying assumptions of our probabilistic graphics program in different ways. [sent-100, score-0.616]

44 TurboTax CAPTCHAs incorporate occlusions that break strokes within 4 (a) (c) (b) (d) (e) (f) Figure 3: Inference over renderer ﬁdelity signiﬁcantly improves the reliability of inference. [sent-101, score-0.381]

45 (a) Reconstruction errors for 5 runs of two variants of our probabilistic graphics program for text. [sent-102, score-0.573]

46 Without sufﬁcient stochasticity and approximation in the generative model — that is, with a strong prior over a purely deterministic, high-ﬁdelity renderer — inference gets stuck in local energy minima (red lines). [sent-103, score-0.714]

47 With inference over renderer ﬁdelity via per-letter and global blur, the tolerance of the image likelihood, and the number of letters, convergence improves substantially (blue lines). [sent-104, score-0.674]

48 Many local minima in the likelihood are escaped over the course of single-variable inference, and the blur variables are automatically adjusted to support localizing and identifying letters. [sent-105, score-0.324]

49 From left to right, we show overall log probability, pixel-wise disagreement (many local minima are escaped over the course of inference), the number of active letters in the scene, and the per-letter blur variables. [sent-108, score-0.299]

50 Inference automatically adjusts blur so that newly proposed letters are often blurred out until they are localized and identiﬁed accurately. [sent-109, score-0.251]

51 The dynamically-adjustable ﬁdelity of our approximate renderer and the high stochasticity of our generative model appear to be necessary for inference to robustly escape local minima. [sent-112, score-0.711]

52 We have observed a kind of self-tuning annealing resulting from inference over the control variables; see Figure 3 for an illustration. [sent-113, score-0.148]

53 We observe robust character recognition given enough inference, with an overall character detection rate of 70. [sent-114, score-0.154]

54 To calibrate the difﬁculty of our corpus, we also ran the Tesseract optical character recognition engine [16] on our corpus; its character detection rate was 37. [sent-116, score-0.154]

55 We have also developed a generative probabilistic graphics program for localizing roads in 3D from single images. [sent-119, score-0.691]

56 As with many perception problems in robotics, there is clear scene structure to exploit, but also considerable uncertainty about the scene, as well as substantial image-to-image variability that needs to be robustly ignored. [sent-121, score-0.271]

57 The probabilistic graphics program we use for this problem is shown in Figure 7. [sent-123, score-0.573]

58 The latent scene S is comprised of the height of the roadway from the ground plane, the road’s width and lane size, and the 3D offset of the corner of the road from the (arbitrary) camera location. [sent-124, score-0.609]

59 The prior encodes assumption that the lanes are small relative to the road, and that the road has two lanes and is very likely to be visible (but may not be centered). [sent-125, score-0.289]

60 This scene is then rendered to produce a surface-based segmentation image, that assigns each input pixel to one of 4 regions r 2 R = {left o↵road, right o↵road, road, lane}. [sent-126, score-0.455]

61 Rendering is done for each scene element separately, followed by compositing, as with our 2D text program. [sent-127, score-0.314]

62 Extensions to richer road and ground geometries are an interesting direction for future work. [sent-129, score-0.221]

63 ASSUME blur (mem (lambda (id) (* 7 (beta 1 2)))) ASSUME global_blur (* 7 (beta 1 2)) ASSUME data_blur (* 7 (beta 1 2)) ASSUME epsilon (gamma 1 1) ASSUME data (load_image "captcha_1. [sent-134, score-0.225]

64 (is_present 10)) OBSERVE (incorporate_stochastic_likelihood data image epsilon) True Figure 4: A generative probabilistic graphics program for reading degraded text. [sent-138, score-0.933]

65 The scene generator chooses letter identity (A-Z and digits 0-9), position, size and rotation at random. [sent-139, score-0.518]

66 These random variables are fed into the renderer, along with the bandwidths of a series of spatial blur kernels (one per letter, another for the overall rendered image from generative model and another for the original input image). [sent-140, score-0.633]

67 These blur kernels control the ﬁdelity of the rendered image. [sent-141, score-0.364]

68 The image returned by the renderer is compared to the data via a pixel-wise Gaussian likelihood model, whose variance is also an unknown variable. [sent-142, score-0.574]

69 ence is that our framework relies on automatic inference techniques, is representationally richer due to compact model description and goes beyond point estimates to report posterior uncertainty. [sent-143, score-0.213]

70 We used these clusters to build a compact appearance model based on cluster-center histograms, by assigning text image pixels to their nearest cluster. [sent-145, score-0.279]

71 Our stochastic likelihood incorporates these histograms, by multiplying together the appearance probabilities for each image region ~ r 2 R. [sent-147, score-0.334]

72 IR =r ID(x,y) ✓r +✏ Zr Figure 5f shows appearance model histograms from one random training frame. [sent-152, score-0.135]

73 Figure 5c shows the extremely noisy lane/non-lane classiﬁcations that result from the appearance model on its own, without our scene prior; accuracy is extremely low. [sent-153, score-0.401]

74 Other, richer appearance models, such as Gaussian mixtures over RGB values (which could be either hand speciﬁed or learned), are compatible with our formulation; our simple, quantized model was chosen primarily for simplicity. [sent-154, score-0.168]

75 We use the same generic Metropolis-Hastings strategy for inference in this problem as in our text application. [sent-155, score-0.155]

76 Although deterministic search strategies for MAP inference could be developed for this particular program, it is less clear how to build a single deterministic search algorithm that could work on both of the generative probabilistic graphics programs we present. [sent-156, score-0.858]

77 In Table 1, we report the accuracy of our approach on one road dataset from the KITTI Vision Benchmark Suite [5]. [sent-157, score-0.221]

78 We report lane/non-lane accuracy results for maximum likelihood classiﬁcation over 10 appearance models (from 10 randomly chosen training images), as well as for the single best appearance model from this set. [sent-160, score-0.291]

79 This baseline system requires signiﬁcant 3D a priori knowledge, including 6 (a) (b) (c) (d) (e) (f) Figure 5: An illustration of generative probabilistic graphics for 3D road ﬁnding. [sent-163, score-0.829]

80 (a) Renderings of random samples from our scene prior, showing the surface-based image segmentation induced by each sample. [sent-164, score-0.45]

81 (c) Maximum likelihood lane/non-lane classiﬁcation of the images from (b) based solely on the best-performing singletraining-frame appearance model (ignoring latent geometry). [sent-166, score-0.244]

82 Geometric constraints are clearly needed for reliable road ﬁnding. [sent-167, score-0.193]

83 (e) Typical inference results from the proposed generative probabilistic graphics approach on the images from (b). [sent-169, score-0.796]

84 (f) Appearance model histograms (over quantized RGB values) from the best-performing single-training-frame appearance model for all four region types: lane, left offroad, right offroad and road. [sent-170, score-0.209]

85 In contrast, our approach has to infer these aspects of the scene from the image data. [sent-173, score-0.405]

86 We also show some uncertainty estimates that result from approximate Bayesian inference in Figure 6. [sent-174, score-0.149]

87 Our probabilistic graphics program for this problem requires under 20 lines of probabilistic code. [sent-175, score-0.691]

88 5 Discussion We have shown that it is possible to write short probabilistic graphics programs that use simple 2D and 3D computer graphics techniques as the backbone for highly approximate generative models. [sent-176, score-1.183]

89 Approximate Bayesian inference over the execution histories of these probabilistic graphics 7 ASSUME road_width (uniform_discrete 5 8) //arbitrary units ASSUME road_height (uniform_discrete 70 150) ASSUME lane_pos_x (uniform_continuous -1. [sent-177, score-0.63]

90 60% Table 1: Quantitative results for lane detection accuracy on one of the road datasets in the KITTI Vision Benchmark Suite [5]. [sent-210, score-0.3]

91 programs — automatically implemented via generic, single-variable Metropolis-Hastings transitions, using existing rendering libraries and simple likelihoods — then implements a new variation on analysis by synthesis [21]. [sent-212, score-0.192]

92 We have also shown that this approach can yield accurate, globally consistent interpretations of real-world images, and can coherently report posterior uncertainty over latent scenes when appropriate. [sent-213, score-0.139]

93 To scale our inference approach to handle more complex scenes, it will likely be important to consider more complex forms of automatic inference, beyond the single-variable Metropolis-Hastings proposals we currently use. [sent-215, score-0.188]

94 For example, discriminatively trained proposals could help, and in fact could be trained based on forward executions of the probabilistic graphics program. [sent-216, score-0.556]

95 Appearance models derived from modern image features and texture descriptors [14, 7, 11] — going beyond the simple quantizations we currently use — could also reduce the burden on inference and improve the generalizability of individual programs. [sent-217, score-0.246]

96 It is important to note that the high dimensionality involved in probabilistic graphics programming does not necessarily mean inference (and even automatic inference) is impossible. [sent-218, score-0.696]

97 For example, approximate inference in models with probabilities bounded away from 0 and 1 can sometimes be provably tractable via sampling techniques, with runtimes that depend on factors other than dimensionality [3]. [sent-219, score-0.149]

98 The most interesting potential of GPGP lies in bringing graphics representations and algorithms to bear on the hard modeling and inference problems in vision. [sent-221, score-0.512]

99 For example, to avoid global rerendering after each inference step, we need to represent and exploit the conditional independencies between latent scene elements and image regions. [sent-222, score-0.552]

100 We hope the GPGP framework facilitates image analysis by Bayesian inversion of rich graphics algorithms for scene generation and image synthesis. [sent-224, score-0.939]

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