Journal of Vision (2011) 11(7):7, 1–33 http://www.journalofvision.org/content/11/7/7 1 On the filter approach to perceptual transparency Franz Faul Institut für Psychologie, Universität Kiel, Germany Vebjørn Ekroll Institut für Psychologie, Universität Kiel, Germany In F. Faul and V. Ekroll (2002), we proposed a filter model of perceptual transparency that describes typical color changes caused by optical filters and accurately predicts perceived transparency. Here, we provide a more elaborate analysis of this model: (A) We address the question of how the model parameters can be estimated in a robust way. (B) We show that the parameters of the original model, which are closely related to physical properties, can be transformed into the alternative parameters hue H, saturation S, transmittance V, and clarity C that better reflect perceptual dimensions of perceived transparency. (C) We investigate the relation of H, S, V, and C to the physical parameters of optical filters and show that C is closely related to the refractive index of the filter, whereas V and S are closely related to its thickness. We also demonstrate that the latter relationship can be used to estimate relative filter thickness from S and V. (D) We investigate restrictions on S that result from properties of color space and determine its distribution under realistic choices of physical parameters. (E) We experimentally determine iso-saturation curves that yield nominal saturation values for filters of different hue such that they appear equally saturated. Keywords: color vision, object recognition, color appearance/constancy Citation: Faul, F., & Ekroll, V. (2011). On the filter approach to perceptual transparency. Journal of Vision, 11(7):7, 1–33, http://www.journalofvision.org/content/11/7/7, doi:10.1167/11.7.7. be investigated in this way, for example, all phenomena Introduction that presumably reflect idiosyncratic strategies used in the visual system, such as grouping processes (Anderson et al., The first systematic empirical studies on perceptual 2006; Koenderink, van Doorn, Pont, & Richards, 2008; transparency were undertaken by members of the Gestalt Koenderink, van Doorn, Pont, & Wijntjes, 2010). school at the beginning of the last century. This is not These direct approaches emphasizeVin our view surprising, because perceptual transparency is a nice correctlyVthe importance of phenomenological criteria, example for their central concept that the whole is but they neglect the potential heuristic value of exploring different from the sum of the parts: The stimulus shown the functional role of vision. In this paper, we pursue a in the top left panel of Figure 1, for example, is not research strategy that takes this into account by consider- interpreted as a mosaic of 8 independent colored regions, ing transparency perception as a detection task. It is based but the circular region is instead seen as a homogeneous on the observation that it is, in general, possible to reliably red transparent layer floating in front of an achromatic infer the presence and properties of external objects from background. However, this transparency interpretation patterns in the proximal stimulus, which implies that each only occurs if the colors in the stimulus are properly visually distinguishable object is characterized by a related to each other (as demonstrated in the right panel of specific signature in the input that can be used as a cue Figure 1). Correspondingly, one of the central goals of in the inference process. To identify “signatures” that may research on perceptual transparency is to identify these be relevant in transparency perception, this approach starts critical color relations and to describe how they determine from objects that usually appear transparent and then the properties of the perceived transparent layer. analyzes the image generation process that “writes” the To solve this problem, one may start directly at the proximal stimulus. The goal is to find formal models that proximal stimulus. Viable strategies to identify relevant describe regularities induced into the input by such color relations are then, for example, to test which of a set objects. Whether a model found in this way describes of candidate transforms of the background colors elicits regularities that are actually used by the visual system as a perceived transparency (D’Zmura, Colantoni, Knoblauch, cue must then be tested empirically. & Laget, 1997) or to try to derive them from empirical There exist two lines of research that both use this data gathered in (matching) experiments (e.g., Anderson strategy but refer to object classes with different image & Khang, 2010; Anderson, Singh, & Meng, 2006; Fulvio, generation processes. The prototypical object in the Singh, & Maloney, 2006; Singh & Anderson, 2002; “episcotister approach” (Da Pos, 1989;Faul,1996; Wollschla¨ger & Anderson, 2009). There are indeed many Gerbino, Stultiens, Troost, & de Weert, 1990; Kasrai & important aspects of transparency perception that can only Kingdom, 2001; Koenderink et al., 2008; Metelli, 1970; doi: 10.1167/11.7.7 Received November 26, 2010; published June 9, 2011 ISSN 1534-7362 * ARVO Downloaded From: https://jov.arvojournals.org/pdfaccess.ashx?url=/data/journals/jov/932798/ on 11/19/2018 Journal of Vision (2011) 11(7):7, 1–33 Faul & Ekroll 2 and that it also raises some theoretical paradoxes (Richards et al., 2009). At the same time, the problems in the filter approach resulting from the involvement of subtractive color mixture have been shown to be much better tractable than initially anticipated. As we have shown in Faul and Ekroll (2002), the color changes occurring when a background is viewed through an optical filter can be described to a good approximation by a filter model that is of similar complexity as the “episcotister model” if smoothly varying, broadband spectra are presupposed. This restriction seems reasonable, because most naturally occurring spectra are restricted in this way. Figure 1. The circular region in the stimulus appears transparent if Interestingly, it turned out that both models often make the colors are chosen properly (left) but opaque if not (right). very similar predictions for the simple stimuli usually used in investigations of perceptual transparency. Given the relative success of the episcotister model in predicting Richards, Koenderink, & Doorn, 2009) is a sector disk transparency, this is a positive finding, but it also makes it (the “episcotister”) that swiftly rotates in front of a difficult to evaluate the relative merits of both models. In nonuniform background. The relevant objects in the “filter Faul and Ekroll, we, therefore, compared both models approach” (Beck, 1978; Beck, Prazdny, & Ivry, 1984; explicitly in cases where the predictions of the models Faul & Ekroll, 2002; Khang & Zaidi, 2002; Nakauchi, differed significantly and obtained strong empirical evi- Silfsten, Parkkinen, & Usui, 1999; Robilotto & Zaidi, dence in favor of the filter model. 2004; Westland & Ripamonti, 2000) are “optical filters,” The filter approach has a number of other attractive like (colored) glass, fluids, and plastics. In the following, properties that motivate exploring it more thoroughly. A we will focus on transparent objects, that is, clear filters. A first strong point of the approach is that transparency more general case are translucent objects, e.g., milky glass, perception is explicitly interpreted as part of a detection which involve light scattering (Brill, 1984; Koenderink task, in which the visual system tries to infer the presence et al., 2008). and subjectively relevant properties of optical filters: By Although most objects we perceive as transparent doing so, one gains an additional set of criteria related to belong to the optical filters class, research based on the the distal side that may be used as guides in identifying a episcotister approach clearly dominates in the literature. plausible model of internal computations used in trans- The episcotister approach appears attractive not only parency perception. These additional criteria basically because it is very simple but also because it seems to be ensure that the model suits its role in this task. Important in fairly good accordance with experimental findings, examples are (a) that the model captures essential especially in the achromatic domain (see, e.g., Kasrai & regularities in the retinal image cast by the relevant Kingdom, 2001). That it often makes rather good objects, (b) that the parameters of the model can be predictions is also documented by the routine use of the robustly estimated from the retinal image, or (c) that they corresponding alpha-blending technique in computer stand in a useful relationship to subjectively important graphics to render transparent overlays. The simplicity of properties of the distal stimulus. the episcotister model stems in part from the fact that it A further methodological advantage is that the filter involves only a form of additive color mixture (partitive approach suggests hypotheses concerning the perception color mixture) so that information about the spectral of transparency in more natural situations than those properties of the scene, which cannot be recovered based traditionally studied. This heuristic value of the filter on the retinal signal, are irrelevant. The filter approach, on approach is a positive aspect of the complexity of the the other hand, may seem much less tractable, because the image generation process: The images cast by optical image generation process associated