MACH BANDS!
Effect of scenario and experience on
interpretation of Mach Bands
What are Mach Bands??
• Ramped changes in
luminance give the
illusion that there is a
pair of thin dark and light
bands.
• Lightness profile shows
that there are no actual
bands.
• Model ganglion cell
output shows presence
of bands, suggesting
that they arise from this
stage of processing.
Some Definitions…
• Luminance: the amount of light
coming from a surface.
• Illumination: The amount of light
falling on the viewed surface.
• Reflectance: the proportion of
incident light that is reflected from
the surface.
• Transmittance: factor affecting
intensity of light that actually
reaches the eyes.
• Luminance = Illumination x
Reflectance
On convolution
• The brain has to average a bunch of inputs coming in
from receptor mosaics. The process through which it does
this is called convolution.
• The receptors in a given mosaic send their outputs into a
second array of elements, which we will call convolution
cells.
• Convolution cells are arranged in convolution arrays, and
carry out a consolidation function with visual processing.
• This replaces the original gray level description with a
smoothed gray level description of the image, said to be
the convolved image.
The Land-horn Theory
• This is a computation worked out to explain how
convolution could work in the brain using the idea of
neurons only having an “on” or “off” level of activity.
• You start with a reflectance profile and superimpose it
onto an illumination profile, represent outputs from
receptors in terms of on-center units and off-center units.
• On-center units will output to “whiteness” arrays, while offcenter units will output to “blackness” arrays.
• The two arrays are then deconvoluted to reconstitute the
image and provide something that the brain can
understand.
The Land-horn Theory
The Land-horn Theory
But why do we care?
• For the most part, we don’t really recognize or
acknowledge Mach Bands in our day-to-day life. We
usually just take them for granted or even ignore them.
• However, one field that this phenomenon is significant in
is radiology, where Mach bands could cause errors in
image interpretation.
• The creation of a Mach Band at the intersection of two
images of differing radiopacities can be misinterpreted as
pathosis in certain situations.
Effect of Scenario and Experience
• Christen Nielsen did a study about
a decade ago that examined this.
• The study asked 33 fourth-year
dental students and 40 dentists to
interpret the same radiograph
involving a maxillary central
incisor under two different
hypothetical scenarios.
Effect of Scenario and Experience
• The presence of this illusion in dental radiology is more
prevalent than one might suspect because it often serves
to enhance edges of anatomical features that might
otherwise be less pronounced.
• Some people see this illusion more vividly than others.
This is somewhat related to the background density effect
as well, where the perceived brightness of an object being
observed is related to the background.
Effect of Scenario and Experience
Instead of just an interface being
accentuated, an entire area is
emphasized by its background.
Effect of Scenario and Experience
Soft tissue borders of the tongue (A) and the
nose (B) against the hard tissue of the jaws
are enhanced by the presence of mach bands
in both cases.
Effect of Scenario and Experience
Effect of Scenario and Experience
• The possible misdiagnosis of mach bands as fracture
lines might be seen wherever abrupt changes in optical
densities occur.
• A student in an Advanced Education in General Dentistry
program, realizing the tendency of cast posts to cause
vertical root fracture, incorrectly diagnosed what turned
out to be simply a mach band in the image as a vertical
root fracture.
• According to Nielsen, the most “disastrous consequence”
of misinterpreting mach band illusions comes when a
dental student or recent graduate is presented with an
emergency situation where a patient has recently
received facial trauma.
Effect of Scenario and Experience
• What is normally recognized as the overlapping of crestal
bone and root is now seen as a radiolucent line (mach
band) representing a horizontal root fracture.
• The student/doctor assumes the crown segment is
nonsalvagable and broken from the root and proceeds to
extract it, only to find out that the root is still attached and
healthy.
• The study compared fourth year dental students with
experienced dentists to see if either group interpreted
more frequently the junction of crestal bone and root
structure as a horizontal root fracture.
Some more x-ray images…
The test image used!
Overlapping of margin of crestal bone
and root creates an illusory radiolucent
line that might be interpreted as a
horizontal root fracture of the maxillary
left central incisor.
Methods and Results
• Two scenarios were presented to the dentists and fourth-
year dental students:
• Scenario 1: A 20-year old male presents with no chief complaint,
other than desiring all six anterior maxillary teeth bleached.
• Scenario 2: An 18-year old male received an elbow to the mouth in
a basketball game. No complaint of pain.
• After reading the scenarios, the participants were asked
what the most likely explanation of what they were looking
at was.
• Of the 17 students given the bleaching scenario, three
interpreted the line as a root fracture, whereas 10 of the
16 students given the trauma scenario saw the line as a
root fracture.
Methods and Results
• Given the bleaching scenario,
only 2 of 21 dentists saw the
line as a fracture. And given
the trauma scenario only 4 of
19 dentists interpreted the line
as a fracture line.
• There was a significant
difference between the
diagnoses depending on
scenario given; both dentists
and students were more likely
to give a diagnosis of fracture
when presented with a trauma
scenario.
• In either scenario, dentists
were less likely to diagnose
fracture.
Discussion
• The results of the study show that students are more likely
than experienced dentists to interpret the cervical crest of
bone as a root fracture.
• The study shows that both students and dentists are
influenced in their diagnosis by the scenario that the
patient presents.
• However, the author believes that experience dentists
who did make a tentative diagnosis of root fracture, after
reviewing the entire picture (patient history, signs and
symptoms, additional radiographs, etc.) would more than
likely make the correct diagnosis and not extract the
crown segment.
My own thoughts…in conclusion
• The scenario presented was interesting and enlightening,
but the experiment itself was constructed poor.
• Sample size too small. More similar to an epidemiological
study than anything else.
• But if you were to expand upon this you could perhaps
explore whether misdiagnosis can “occur” at a higher
level of visual processing or at a lower level.