In a previous work (X. Otazu, M. Vanrell, & C. A. Párraga, 2008b), we showed how several brightness induction effects can be predicted using a simple multiresolution wavelet model (BIWaM). Here we present a new model for chromatic induction processes (termed Chromatic Induction Wavelet Model or CIWaM), which is also implemented on a multiresolution framework and based on similar assumptions related to the spatial frequency and the contrast surround energy of the stimulus. The CIWaM can be interpreted as a very simple extension of the BIWaM to the chromatic channels, which in our case are defined in the MacLeod–Boynton (*lsY*) color space. This new model allows us to unify both chromatic assimilation and chromatic contrast effects in a single mathematical formulation. The predictions of the CIWaM were tested by means of several color and brightness induction experiments, which showed an acceptable agreement between model predictions and psychophysical data.

*White effect*, grating induction, the

*Todorovic effect*,

*Mach bands*, the

*Chevreul effect*, and the

*Adelson–Logvinenko tile effects*, along with other previously unexplained effects such as the

*dungeon illusion*(Bressan, 2001), using a single set of parameters and only three basic assumptions. The BIWaM unified brightness contrast and assimilation effects, modeling them as a single perceptual process. Brightness contrast describes a shift of the test stimulus brightness away from its surroundings and brightness assimilation describes the opposite (the brightness of the test stimulus shifts toward that of its surroundings).

*en masse*, can have both good predictive and explanatory power.

*Assumption 1: spatial frequency*. The induction effect operating on a stimulus of a particular SF in a given chromatic or achromatic channel is determined by the characteristics of its surround stimuli with the same SF (within an octave).

*Assumption 2: spatial orientation*. Assimilation in a given chromatic or achromatic channel is stronger when both the central stimulus and the surround stimulus have similar orientations. The opposite occurs for contrast effects. Consequently, when relative spatial orientation between stimulus and surround is orthogonal, assimilation of the central stimulus is the weakest and contrast is the strongest.

*Assumption 3: surround contrast energy*. Assimilation in a given chromatic or achromatic channel increases when the contrast energy of the surrounding features increases. Conversely, the contrast effect decreases when surround contrast energy increases.

*Assumption 4: channel independence and combination*. The global induction effect at a given point is the result of the vector addition (in the chromatically opponent space) of the induction effects occurring independently in each color pathway.

*I*is the original image,

*ω*

_{ s,o }are the given component images, also called wavelet planes,

*n*represents different spatial frequencies, and

*c*

_{ n }is the residual. Each plane contains the component of

*I*with a given orientation

*o*, at a specific spatial frequency

*s*. Although Assumption 2 is not tested here, we have used three different orientations,

*o*=

*h*,

*v*,

*d*to represent 0, 90, and 45 degrees, respectively, to maintain consistency with our previous work.

*α*). This weighting function, which depends on two parameters, the spatial frequency of the plane considered and the ratio of contrast energy between each stimulus feature and its surrounds, allows us to recover the

*perceived*or

*induced*image

*I*

^{ p }, from the decomposition of the original image (Equation 1). The resulting

*I*

^{ p }is obtained by computing

*α*

_{ s,r,o }, which modifies the coefficients obtained from the wavelet decomposition and is responsible for introducing the induction effects, is not a traditional weighting function, since its effects are dependent on the surrounding contrast acting on every single feature within each wavelet plane. As a consequence, for each pixel in the image, the weighting effects will act as stated by the Model Assumptions 1 to 3.

*α*

_{ s,r,o }. Before we continue with the requirements for Assumption 4, we need first to review other ways in which this weighting function can be understood. Thus, in the next section we will attempt to provide a more thorough interpretation of

*α*

_{ s,r,o }, and following this, we will continue with our extension of the model to the color domain.

*extended CSF*

*α*

_{ s,r,o }, is the main component responsible for most of the differences between the physical image and the output or

*perceived*image. There are several constraints to

*α*

_{ s,r,o }. For start, we need to define a threshold SF value above which assimilation phenomenon overtakes contrast phenomenon (Smith, Jin, & Pokorny, 2001), with a shape resembling the well-known human CSF (Mullen, 1985) so that the CSF turns out to be a special case of the

*α*

_{ s,r,o }when there is no center–surround energy unbalance (i.e.,

*r*= 1). We decided to name this function,

*extended*CSF (or ECSF). Our previous work in brightness induction supported an ECSF that is low-pass when surround contrast energy is predominant and becomes band-pass when center contrast energy is predominant (Otazu et al., 2008b). For this reason, we decided to reformulate the weighting function that forms the core of BIWaM, generalizing it to include color phenomena. In the present analysis, we will assume that

*α*

_{ s,r,o }depends on just two variables: the center–surround contrast energy ratio

*r*and the spatial frequency

*s*. Given that we did not test the real implications of Assumption 2, here we will suppose that the ECSF is independent of spatial orientation (its dependency of spatial orientation will be studied in detail in the future).

*s*in terms of the stimulus visual angle and denote it as

*ν*(in cycles per degree). The function we have selected for our model is displayed in Figure 1 (top panel), where the values of

*α*are shown in terms of

*r*and

*ν*, that is

*α*(

*ν*,

*r*).

*r*, we can generate a family of weighting functions across all spatial frequencies, as shown in Figure 1 (bottom panel).

*r*varies at each point in the image. This newly introduced concept of a spatially variant CSF needs to be studied in more detail if we aspire to accurately model complex chromatic induction processes, since additional studies may reveal dependency on other factors such as overall scene intensity, the interaction between chromatic and achromatic channels, temporal adaptation, etc. However, as a first approximation, we will adopt an ECSF similar to the weighting function described previously (Otazu et al., 2008b).

*υ*

_{0}= 4 cpd was adopted for the

*luminance*channel and

*υ*

_{0}= 2 cpd for the

*red–green*and

*blue–yellow*chromatic channels according to psychophysical measures of both the peak of the human CSF (Mullen, 1985) and the transition point between assimilation and contrast (Fach & Sharpe, 1986; Simpson & McFadden, 2005; Smith et al., 2001; Walker, 1978). Both

*σ*

_{2}and

*σ*

_{3}were set to 1.25 and 2, respectively. To simulate the band-pass profile of the intensity channel's CSF and the low-pass profile of chromatic channels' CSF (Mullen, 1985), we set

*σ*

_{1}= 1.25 for the luminance channel, and

*σ*

_{1}= 2 for both the

*red–green*and

*blue–yellow*chromatically opponent channels.

*α*(

*ν*,

*r*) for the luminance channel. To avoid

*α*(

*ν*,

*r*) becoming null at low spatial frequencies, we introduced the term

*α*

_{min}(

*ν*,

*r*) so that

*α*(

*ν*,

*r*) →

*α*

_{min}(

*ν*,

*r*) when

*r*→ 0. This avoids a high degree of assimilation being performed at low SF (i.e., large-scale features), which would make parts of the image to reach zero value. Similarly,

*α*

_{min}(

*ν*,

*r*) → 1 when

*ν*≪

*ν*

_{0}(i.e., the lowest SFs), which implies

*α*(

*ν*,

*r*) → 1.

*l*,

*s*, and ϒ, where the last represents luminance and is expressed in candelas per square meters; Boynton, 1986). This color space is based on a decomposition of the visual stimulus in three wavelength sensitive components (L, M, and S for long, middle, and short wavelengths as determined by Smith & Pokorny, 1975), which reflects the relative excitations of the human photoreceptors. It is also directly related to the physiology of the primate visual pathways and cortex in terms of post-receptoral color opponent signals, represented as orthogonal chromatic and achromatic axes (Derrington, Krauskopf, & Lennie, 1984).

*l*,

*s*, and ϒ channel representations of the original image in the MacLeod–Boynton space. In this context, the processing of the ϒ channel by BIWaM is not different from the work already published (Otazu et al., 2008b). In the case of the

*l*and

*s*channels, we used a different ECSF (the same for both channels) because the spatial transfer characteristics of the chromatic channels are different from that of the achromatic channel (being the later band-pass in SF and the former low-pass; Mullen, 1985). At the moment, we make no distinction between the spatial transfer characteristics of the two chromatic channels. Whether a different mathematical expression should be used for each of the three color channels has to be determined in the future.

*l*represents the “L vs. M” (or

*red–green*) cone opponency and the ordinate

*s*represents the “S vs. (L + M)” (or

*blue–yellow*) cone opponency (where

*s*is normalized to unity

*equal-energy*white). The scaling of the

*s*-axis in the MacLeod–Boynton space is essentially arbitrary (Boynton, 1986). However, we believe this does not impact on the generality of our results since CIWaM is based on a multiresolution computation that does not operate directly on absolute values (e.g., cone activations or luminance) but on dimensionless magnitudes such as contrast energy, which are always calculated relative to their surroundings.

*reference stimulus*) consisted of a series of concentric rings alternating between two chromaticities with an extra ring of similar width (namely the

*reference ring*) as shown in Figure 2. For the reader who is familiar with the experiments of Monnier and Shevell (to which the present experiments are closely related), we want to stress that the naming convention for “test” and “reference” (or “comparison”) rings adopted here is opposite to theirs.

*inducers*, according to their physical proximity to the test ring. When the two inducers were chosen to have the same chromaticity, they formed a uniform chromatic background. The right side stimulus (the

*test stimulus*) always consisted of a

*test ring*(same size as the reference ring) placed over a uniform achromatic background approximately metameric to equal-energy white (

*l*= 0.66,

*s*= 0.98, ϒ = 27.5; Boynton, 1996; Monnier & Shevell, 2004). Both the chromaticities of the reference and inducer rings and the number of annuli on the reference stimulus were determined for each experimental condition according to Table 1. The chromaticities (in the MacLeod–Boynton space) corresponding to these conditions are shown in Figures 3 and 4.

Conditions | Reference ring | 1st inducer | 2nd inducer | ||||||
---|---|---|---|---|---|---|---|---|---|

l | s | ϒ | l | s | ϒ | l | s | ϒ | |

Experiment 1 (striped background) | |||||||||

1 | 0.66 | 0.98 | 27.5 | 0.64 | 1.40 | 20.0 | 0.68 | 0.60 | 37.0 |

2 | 0.67 | 1.00 | 26.0 | 0.64 | 1.40 | 20.0 | 0.64 | 0.60 | 32.0 |

3 | 0.66 | 0.98 | 27.5 | 0.68 | 1.40 | 22.0 | 0.64 | 0.60 | 32.0 |

4 | 0.65 | 1.00 | 30.0 | 0.68 | 1.40 | 22.0 | 0.68 | 0.60 | 37.0 |

Experiment 2 (uniform background) | |||||||||

1 | 0.64 | 1.00 | 26.0 | 0.64 | 0.60 | 32.0 | 0.64 | 0.60 | 32.0 |

2 | 0.66 | 0.60 | 34.5 | 0.68 | 0.60 | 37.0 | 0.68 | 0.60 | 37.0 |

3 | 0.68 | 1.00 | 29.5 | 0.68 | 1.40 | 22.0 | 0.68 | 1.40 | 22.0 |

4 | 0.66 | 1.40 | 21.0 | 0.64 | 1.40 | 20.0 | 0.64 | 1.40 | 20.0 |

*experiments*with three different

*spatial configurations*consisting of rings of different widths each. The rings' widths were obtained by diving the reference stimulus width (see Figure 2) in 5, 11, or 17 parts. These spatial configurations of rings are subsequently referred as conf1, conf2, and conf3. The spatial frequencies of each of these configurations are 0.81, 1.77, and 2.74 cpd, respectively. The stimulus rings were rendered using four sets of colored patterns (also referred as

*conditions*: see details in Table 1).

*ls*ϒ MacLeod–Boynton cone space in an intuitive way (left =

*greener*, right =

*redder*, front =

*bluer*, back =

*yellower*, up =

*lighter*, down =

*darker*). There were no time constraints to the matching procedure and fixation was free with 10-s intervals between runs.

*l*and

*s*chromatic axes (since the scaling of

*s*is arbitrary), preliminary experiments showed that this amount was noticeable enough to serve the purpose of randomizing the starting point.

**t**to its final value

**t**

_{test}so that its color is perceived the same as the reference ring's color

**t**

_{ref}, e.g.,

**t**′

_{ref}≅

**t**′

_{test}, where

**t**′

_{ref}and

**t**′

_{test}are the perceived reference and test ring colors, respectively. To evaluate the accuracy of CIWaM, we apply it to the final image (obtained psychophysically), resulting in a CIWaM estimation of the colors perceived by the observers on both reference and test rings, i.e.,

**t**

^{CIWaM}

_{ref}and

**t**

^{CIWaM}

_{test}, respectively.

**t**

_{test}are distributed over the chromaticity plane, they have a standard deviation

*σ*

_{test}and correspondingly, the distribution of CIWaM-estimated values

**t**

^{CIWaM}

_{test}has a corresponding standard deviation

*σ*

^{CIWaM}

_{test}. In Figure 6, we show the average

**t**

^{CIWaM}

_{test}values (colored void squares) with the corresponding error bars (standard deviation

*σ*

^{CIWaM}

_{test}) alongside

**t**

^{CIWaM}

_{ref}values (filled squares). Following the previous convention, colors of the reference and inducer rings (as detailed in Table 1 and Figure 4) are shown in empty black symbols. We also adopted a new convention regarding the three different configurations (as detailed in the Experimental procedure section): configuration 1 (or conf1) is always shown in red symbols, configuration 2 (or conf2) in blue symbols, and configuration 3 (or conf3) in green symbols.

**t**

^{CIWaM}

_{ref}≅

**t**

^{CIWaM}

_{test}, that is, a zero difference between CIWaM-estimated colors for both the reference and test rings, hence filled and void squares in Figure 6 would coincide. In the Discussion section, we will analyze the correspondence of these two values.

- Define test stimulus image
*I*(**r**and**t**are the colors of the reference and test rings, respectively). - Use image
*I*as input to CIWaM to obtain a simulated “perceived” image*I*_{0}. - From
*I*_{0}calculate the mean perceived colors**r**′ and**t**′ of the reference and test rings, respectively. - Calculate perceptual difference
**d**′ =**r**′ −**t**′, being**d**′ the vector (*d*_{ l },*d*_{ s },*d*_{ϒ}). - Define a new test ring color
**t**=**t**+ 0.6 ***d**′. - If
*d*_{ l }<*ɛ*_{ l },*d*_{ s }<*ɛ*_{ s }, and*d*_{ϒ}<*ɛ*_{ϒ}, then return**t**_{CIWaM}≡**t**as the final value fitted else go to step 1.

**r**and

**t**as the psychophysical experiment (see Methods section), i.e., the same initial stimulus image. From this input image, CIWaM observer obtains a “perceived” image from which we calculate the color difference between reference and test rings.

*a priori*three values (

*ɛ*

_{ l },

*ɛ*

_{ s }, and

*ɛ*

_{ϒ}), which are the maximum allowed difference between the perceived reference and test rings for each chromatic channel. When the differences are lower than these values, we consider that the rings are the same color and stop the iterations. In our particular case, we used

*ɛ*

_{ l }= 0.0001,

*ɛ*

_{ s }= 0.001, and

*ɛ*

_{ϒ}= 0.05 (Figure 7).

**t**

_{CIWaM}for the test ring, which can be compared to the color

**t**

_{test}obtained from the psychophysical experiments. We want to stress that in this notation the sub-index denotes the physical values obtained by the simulated CIWaM observer, whereas the super-index denotes the perceived values obtained by CIWaM.

**t**

_{test}and their corresponding CIWaM observer predictions

**t**

_{CIWaM}are displayed in Figures 8–10. We adopted the convention of showing

**t**

_{CIWaM}as filled circles, with the empty circles indicating the results obtained by

**t**

_{test}(observers). The error bars on the plots show the standard deviation of our experimental results. In Figure 10, which shows several results in the same plot, we added arrows to illustrate which model prediction is connected to which experimental result.

**t**

_{test}approximately lie on the diagonal line that joins the reference ring color (void black circle) with the two inducers (extremes of the diagonal line). CIWaM observer predicted values

**t**

_{CIWaM}also approximately lie on this diagonal line and they are close to the corresponding psychophysically obtained values for the three spatial configurations tested (shown in red, blue, and green symbols). In addition, the quantitative distribution of these points according to spatial configuration is similar, e.g., conf1 (5 stripes) results are higher on the

*l*-axis and lower on the

*s*-axis; conf3 (17 stripes) results are lower on the

*l*-axis and higher on the

*s*-axis, mimicking the psychophysics. A similar agreement also occurs in the ϒ-axis (not shown, given that CIWaM is the same as the already tested BIWaM; Otazu et al., 2008b), confirming our hypothesis of independence between achromatic and chromatic channels.

**t**

_{test}is termed

_{test}and includes all the experiments, configurations, and conditions shown in Table 2 (first row). When we apply CIWaM to each of the psychophysical solutions, we obtain a distribution of values with an average value

**t**

^{CIWaM}

_{test}, a standard deviation

*σ*

^{CIWaM}

_{test}, and correspondingly, for each reference ring we obtain a value

**t**

^{CIWaM}

_{ref}(with no standard deviation).

l | s | ϒ | |
---|---|---|---|

σ ― _{test} | 0.0037 | 0.0741 | 1.8846 |

σ ― ^{CIWaM} _{test} | 0.0082 | 0.1633 | 4.3160 |

σ ^{CIWaM} _{ref–test} | 0.0077 | 0.0947 | 3.4563 |

**t**

^{CIWaM}

_{ref}≅

**t**

^{CIWaM}

_{test}). The differences between the predicted values of the reference and test rings are the distances between a void square and its corresponding filled square in Figure 6.

**t**

^{CIWaM}

_{ref–test}=

**t**

^{CIWaM}

_{ref}−

**t**

^{CIWaM}

_{test}on the

*ls*plane in Figure 11, which are distributed around (

*l*,

*s*, ϒ) = (0, 0, 0), their ideal location. A similar distribution was obtained for the ϒ channel. On the third row of Table 2, we show the standard deviation of the values plotted in Figure 11 (

*σ*

^{CIWaM}

_{ref–test}), which can be interpreted as the error of CIWaM. In order to get an estimation of the significance of this error, the second row of Table 2 shows the mean standard deviation of observer responses (

^{CIWaM}

_{test}) in all three channels. Table 2 allows us to compare the uncertainty of the model (

*σ*

^{CIWaM}

_{ref–test}) to the uncertainty of the observer responses (

^{CIWaM}

_{test}), showing that they are of similar magnitude.

**t**

^{CIWaM}

_{ref}(abscissa) versus the CIWaM-estimated final test ring color

**t**

^{CIWaM}

_{test}(ordinate) for all experiments, conditions, and subjects in each of the

*l*,

*s*, and ϒ chromatic channels. There are 24 points in each plot (2 experiments × 3 configurations × 4 conditions). The dotted line (diagonal) is where all points should lie if CIWaM's predictions were 100% accurate.

*c*≅ 0.9. The mean squares of the residuals

*r*

^{2}is also shown for every channel in the figure.

*l*- and

*s*-axes of the central plots in Figures 8 and 13, the corresponding red–green and blue–yellow channel stimuli as “seen” by the model. In this section, we will analyze each experiment separately, with the aim of understanding more in detail the operation of the model.

*l*channel, and the one seen by the model's

*s*channel) are surrounded by different sets of inducer rings (1st and 2nd inducers). The signals from these inducer rings are markedly different, implying relatively high surround contrast energy (

*l*

_{1}

*s*

_{1}ϒ

_{1}= [0.64, 1.40, 20.0];

*l*

_{2}

*s*

_{2}ϒ

_{2}= [0.64, 1.40, 20.0]). For a complete list of chromaticity values, see Table 1.

*Assumption 3*, assimilation increases with increased surround contrast, i.e., the reference ring tends to the value of the 1st inducer ring in both the

*l*and

*s*channels. This is primarily the reason why both the psychophysical values (empty circles) and CIWaM predictions (filled circles) lie along the diagonal that joins the reference ring and the first inducer ring colors: test ring chromatic values approach that of the 1st inducer.

*l*and

*s*channels. In Figure 8a, we can see that the assimilation effect is stronger or weaker depending on the ring's size and spatial configuration, being the lower SF result (conf1, red symbols) further away from the first inducer and the higher SF results (conf3, in green) closer along the diagonal. The dependency of these effects on spatial configuration is mainly because of the extended CSF behavior: a higher response on lower spatial frequencies (e.g., conf1, which implies lower assimilation and higher contrast) and a lower response on higher frequencies (e.g., conf3, which implies higher assimilation and lower contrast). Since these effects are applied simultaneously to both

*l*and

*s*channels using the same rule, the final result lies on the chromaticity diagonal.

*l*channel. These results (and the model's behavior) were initially unexpected by the authors, who anticipated the colored points of the plot to be aligned toward the 1st inducer, not to be shifted toward the right side. However, it is possible to qualitatively explain these results again bearing in mind

*Assumption 3*. In the

*s*chromatic channel, the reference ring has high surround contrast energy because of the different

*s*values between the 1st and 2nd inducer rings. However, in the

*l*chromatic channel, the first and second inducer rings have the same value, which means that the reference ring is on a uniform “

*l*” background (see image next to the

*l*channel). A uniform background on the

*l*channel yields null surround contrast energy for the reference ring in that channel, which by means of

*Assumption 3*implies that on the

*l*channel contrast is high (i.e., it shifts away from the first inducer) and assimilation is low (i.e., it shifts toward the first inducer). Because of that, the

*l*chromaticity value of the reference ring moves away from that of the first inducer (it has a higher

*l*value). On the other hand, on the

*s*channel the surround contrast energy is high, inducing assimilation (i.e., the reference–test rings move toward the 1st inducer). The combined effects on both channels is that the resulting reference ring chromaticity becomes higher on the

*l*channel

*and*on the

*s*channel (i.e., it shifts toward the top right corner of the figure), which is different to what was expected from the previous results.

**t**

_{test}until the new perceived color

**t**′

_{test}is equal to the color

**t**′

_{ref}he perceives when observing the reference ring (color

**t**

_{ref}). Here both perceptual colors

**t**′

_{ref}and

**t**′

_{test}are influenced by their respective backgrounds. At the end of the run, we have

**t**′

_{test}≅

**t**′

_{ref}.

**t**

_{test}as obtained by both human observers (void colored circles with error bars) in condition 1 for all spatial configurations. These results are outside the reference–test line (as determined by the void black circle and square representing the reference–inducer background color). The shift induced by the colored uniform background on the reference ring color

**t**

_{ref}as predicted by CIWaM observer is represented as a light blue dashed arrow (

**t**′

_{ref}). However, it is when the induction effects of the gray uniform background on the test ring

**t**

_{test}are taken into account that a complete explanation emerges. In fact, CIWaM can perform an estimation of these perceptual

**t**′

_{test}and

**t**′

_{ref}colors. These are the

**t**

^{CIWaM}

_{test}and

**t**

^{CIWaM}

_{ref}values shown under the Analysis 1 heading in the Results section as filled squares in Figure 6.

**t**

_{test}is represented in Figure 13 as a solid gray arrow. This color difference exerts the same effect on the test colors as the inducer–reference difference exerts in the reference colors: both arrows “push” their respective colors along their own axis and meet somewhere at the top. The color of the left ring

**t**

_{ref}shifts to become

**t**′

_{ref}and the color of the right ring

**t**

_{test}becomes

**t**′

_{test}where the subject sees them as equal, e.g.,

**t**′

_{test}≅

**t**′

_{ref}. The effect of the gray background is apparent from the psychophysical results and is also reproduced by CIWaM.

**t**

_{test}and the CIWaM predictions

**t**

_{CIWaM}in the

*ls*chromatic plane, i.e.,

**t**

_{CIWaM–test}≡

**t**

_{CIWaM}−

**t**

_{test}(24 points: 2 experiments × 3 configurations × 4 conditions). We can see that they are randomly distributed around the ideal

**t**

_{CIWaM–test}= (0, 0, 0) and present a pattern similar to that of Figure 11 (again, we only show the

*ls*chromatic plane to ease the visualization). In Table 3 (first row), we show the mean standard deviation of the psychophysical results (

_{test}) for all three

*ls*ϒ channels. The second row shows the equivalent for the difference between model predictions and observers (the model's uncertainty,

*σ*

_{CIWaM–test}). These figures show that both are in good agreement. These results provide simple verification of Assumption 3 (influence of the surround contrast) in the model.

l | s | ϒ | |
---|---|---|---|

σ ― _{test} | 0.0037 | 0.0741 | 1.8846 |

σ _{CIWaM–test} | 0.0034 | 0.0417 | 1.4981 |

l | s | ϒ | |
---|---|---|---|

σ ^{CIWaM} _{ref–test}/ σ ― ^{CIWaM} _{test} | 0.9081 | 0.5634 | 0.7949 |

σ _{CIWaM–test}/ σ ― _{test} | 0.9374 | 0.5799 | 0.8008 |

**t**

_{CIWaM}(abscissa) versus the psychophysical results

**t**

_{test}(ordinate) for all experiments, and configurations in each of the

*l*,

*s*, and ϒ chromatic channels. There are 24 points in each plot (2 experiments × 3 configurations × 4 conditions). Each point represents the mean value of a given experiment, condition, and configuration for all observers. The dotted line (diagonal) is where all points should lie if CIWaM's predictions were 100% accurate.

*c*≅ 0.95. The mean squares of the residuals

*r*

^{2}is also shown for every channel in the corresponding figure.

*s*since the

*s*-component of the test ring color tends to the

*s*value of the first inducer, i.e., the color of the test ring is shifted in the vertical direction. However, in channel

*l*the opposite effect occurs since the

*l*value of the test ring goes away from the

*l*value of the first inducer, i.e., the color of the test ring is shifted in the horizontal direction. As a result, the vector combination of these components does not necessarily lie in the line joining the test and the first inducer. Furthermore, we may ask what kind of effect it is, whether to call it a chromatic assimilation, a chromatic contrast, or both.

*r*= 1) of the ECSF.

Experiment 1 results | |||
---|---|---|---|

l | s | ϒ | |

Cond1 | |||

Conf1 | 0.660 | 0.981 | 26.3 |

Conf2 | 0.655 | 1.108 | 24.1 |

Conf3 | 0.650 | 1.231 | 23.3 |

Cond2 | |||

Conf1 | 0.672 | 0.980 | 24.8 |

Conf2 | 0.675 | 1.062 | 24.2 |

Conf3 | 0.674 | 1.146 | 23.9 |

Cond3 | |||

Conf1 | 0.661 | 1.003 | 26.5 |

Conf2 | 0.666 | 1.087 | 25.3 |

Conf3 | 0.669 | 1.201 | 23.5 |

Cond4 | |||

Conf1 | 0.646 | 1.019 | 28.5 |

Conf2 | 0.644 | 1.173 | 27.2 |

Conf3 | 0.641 | 1.307 | 25.0 |

Experiment 1 standard deviations | |||
---|---|---|---|

l | s | ϒ | |

Cond1 | |||

Conf1 | 0.002 | 0.05 | 2.6 |

Conf2 | 0.004 | 0.12 | 2.4 |

Conf3 | 0.008 | 0.19 | 3.1 |

Cond2 | |||

Conf1 | 0.003 | 0.04 | 1.2 |

Conf2 | 0.004 | 0.07 | 2.4 |

Conf3 | 0.005 | 0.11 | 1.8 |

Cond3 | |||

Conf1 | 0.004 | 0.07 | 2.3 |

Conf2 | 0.003 | 0.08 | 2.4 |

Conf3 | 0.004 | 0.13 | 3.1 |

Cond4 | |||

Conf1 | 0.004 | 0.06 | 2.8 |

Conf2 | 0.004 | 0.06 | 2.0 |

Conf3 | 0.005 | 0.12 | 2.2 |

Experiment 2 results | |||
---|---|---|---|

l | s | ϒ | |

Cond1 | |||

Conf1 | 0.650 | 1.152 | 22.8 |

Conf2 | 0.651 | 1.185 | 22.4 |

Conf3 | 0.650 | 1.184 | 22.5 |

Cond2 | |||

Conf1 | 0.646 | 0.809 | 27.6 |

Conf2 | 0.644 | 0.815 | 26.5 |

Conf3 | 0.642 | 0.807 | 26.8 |

Cond3 | |||

Conf1 | 0.670 | 0.867 | 31.4 |

Conf2 | 0.671 | 0.867 | 31.3 |

Conf3 | 0.671 | 0.868 | 31.5 |

Cond4 | |||

Conf1 | 0.670 | 1.116 | 26.5 |

Conf2 | 0.670 | 1.125 | 27.6 |

Conf3 | 0.669 | 1.165 | 27.1 |

Experiment 2 standard deviations | |||
---|---|---|---|

l | s | ϒ | |

Cond1 | |||

Conf1 | 0.002 | 0.05 | 1.7 |

Conf2 | 0.003 | 0.06 | 1.2 |

Conf3 | 0.002 | 0.08 | 0.8 |

Cond2 | |||

Conf1 | 0.003 | 0.03 | 1.8 |

Conf2 | 0.006 | 0.05 | 1.4 |

Conf3 | 0.005 | 0.07 | 1.7 |

Cond3 | |||

Conf1 | 0.003 | 0.04 | 1.8 |

Conf2 | 0.002 | 0.04 | 1.9 |

Conf3 | 0.003 | 0.05 | 1.4 |

Cond4 | |||

Conf1 | 0.004 | 0.05 | 1.4 |

Conf2 | 0.003 | 0.07 | 0.8 |

Conf3 | 0.002 | 0.08 | 1.3 |