Weber contrast

Weber contrast is defined as

${\displaystyle {\frac {I-I_{\mathrm {b} }}{I_{\mathrm {b} }}},}$

with ${\displaystyle I}$ and ${\displaystyle I_{\mathrm {b} }}$ representing the luminance of the features and the background, respectively.^[4] The measure is also referred to as Weber fraction, since it is the term that is constant in Weber's Law. Weber contrast is commonly used in cases where small features are present on a large uniform background, i.e., where the average luminance is approximately equal to the background luminance.

Michelson contrast

Michelson contrast^[6] (also known as the visibility) is commonly used for patterns where both bright and dark features are equivalent and take up similar fractions of the area (e.g. sine-wave gratings). The Michelson contrast is defined as^[4]

${\displaystyle {\frac {I_{\mathrm {max} }-I_{\mathrm {min} }}{I_{\mathrm {max} }+I_{\mathrm {min} }}},}$

with ${\displaystyle I_{\mathrm {max} }}$ and ${\displaystyle I_{\mathrm {min} }}$ representing the highest and lowest luminance. The denominator represents twice the average of the maximum and minimum luminances.^[7]

This form of contrast is an effective way to quantify contrast for periodic functions f(x) and is also known as the modulation m_f of a periodic signal f. Modulation quantifies the relative amount by which the amplitude (or difference) (f_max − f_min)/2 of f stands out from the average value (or background) (f_max + f_min)/2. In general, m_f refers to the contrast of the periodic signal f relative to its average value. If m_f = 0, then f has no contrast. If two periodic functions f and g have the same average value, then f has more contrast than g if m_f > m_g.^[8]

RMS contrast

Root mean square (RMS) contrast does not depend on the spatial frequency content or the spatial distribution of contrast in the image. RMS contrast is defined as the standard deviation of the pixel intensities:^[4]

${\displaystyle {\sqrt {{\frac {1}{MN}}\sum _{i=0}^{N-1}\sum _{j=0}^{M-1}\left(I_{ij}-{\bar {I}}\right)^{2}}}}$

where intensities ${\displaystyle I_{ij}}$ are the ${\displaystyle i}$-th ${\displaystyle j}$-th element of the two-dimensional image of size ${\displaystyle M}$ by ${\displaystyle N}$. ${\displaystyle {\bar {I}}}$ is the average intensity of all pixel values in the image. The image ${\displaystyle I}$ is assumed to have its pixel intensities normalized in the range ${\displaystyle [0,1]}$.

Contrast sensitivity and visual acuity

Log–log plot of spatial contrast sensitivity functions for luminance and chromatic contrast

Visual acuity is a parameter that is frequently used to assess overall vision. However, diminished contrast sensitivity may cause decreased visual function in spite of normal visual acuity.^[10] For example, some individuals with glaucoma may achieve 20/20 vision on acuity exams, yet struggle with activities of daily living, such as driving at night.

As mentioned above, contrast sensitivity describes the ability of the visual system to distinguish bright and dim components of a static image. Visual acuity can be defined as the angle with which one can resolve two points as being separate since the image is shown with 100% contrast and is projected onto the fovea of the retina.^[11] Thus, when an optometrist or ophthalmologist assesses a patient's visual acuity using a Snellen chart or some other acuity chart, the target image is displayed at high contrast, e.g., black letters of decreasing size on a white background. A subsequent contrast sensitivity exam may demonstrate difficulty with decreased contrast (using, e.g., the Pelli–Robson chart, which consists of uniform-sized but increasingly pale grey letters on a white background).

To assess a patient's contrast sensitivity, one of several diagnostic exams may be used. Most charts in an ophthalmologist's or optometrist's office will show images of varying contrast and spatial frequency. Parallel bars of varying width and contrast, known as sine-wave gratings, are sequentially viewed by the patient. The width of the bars and their distance apart represent spatial frequency, measured in cycles per degree (cpd or cyc/deg).

Studies have demonstrated that medium-level spatial frequency, approximately 5–7 cyc/deg, is optimally detected by most individuals, compared with low- or high-level spatial frequencies.^[12] Contrast threshold can be defined as the minimum contrast that can be resolved by the patient. Contrast sensitivity is typically expressed as the reciprocal of the threshold contrast for detection of a given pattern (i.e., 1 ÷ contrast threshold).^[13]

Using the results of a contrast sensitivity exam, a contrast sensitivity curve can be plotted, with spatial frequency on the horizontal, and contrast threshold on the vertical axis. Also known as contrast sensitivity function (CSF), the plot demonstrates the normal range of contrast sensitivity, and will indicate diminished contrast sensitivity in patients who fall below the normal curve. Some graphs contain "contrast sensitivity acuity equivalents", with lower acuity values falling in the area under the curve. In patients with normal visual acuity and concomitant reduced contrast sensitivity, the area under the curve serves as a graphical representation of the visual deficit. It can be because of this impairment in contrast sensitivity that patients have difficulty driving at night, climbing stairs and other activities of daily living in which contrast is reduced.^[14]

The graph demonstrates the relationship between contrast sensitivity and spatial frequency. The target-like images are representative of center-surround organization of neurons, with peripheral inhibition at low, intermediate and high spatial frequencies. Used with permission from Brian Wandell, PhD.

Recent studies have demonstrated that intermediate-frequency sinusoidal patterns are optimally-detected by the retina due to the center-surround arrangement of neuronal receptive fields.^[15] In an intermediate spatial frequency, the peak (brighter bars) of the pattern is detected by the center of the receptive field, while the troughs (darker bars) are detected by the inhibitory periphery of the receptive field. For this reason, low- and high-spatial frequencies elicit excitatory and inhibitory impulses by overlapping frequency peaks and troughs in the center and periphery of the neuronal receptive field.^[16] Other environmental,^[17] physiologic and anatomical factors influence the neuronal transmission of sinusoidal patterns, including adaptation.^[18]

Decreased contrast sensitivity arises from multiple etiologies, including retinal disorders such as age-related macular degeneration (ARMD), amblyopia, lens abnormalities, such as cataract, and by higher-order neural dysfunction, including stroke and Alzheimer's disease.^[19] In light of the multitude of etiologies leading to decreased contrast sensitivity, contrast sensitivity tests are useful in the characterization and monitoring of dysfunction, and less helpful in detection of disease.