The phenomenon in question is part of attention, specifically endogenous orienting, or willful focusing of cognitive capacities on particular stimuli or sensory regions (of body or environment). From Wikipedia:
Orienting attention is vital and can be controlled through external (exogenous) or internal (endogenous) processes.
The first aspect is called bottom-up processing, also known as stimulus-driven attention or exogenous attention. These describe attentional processing which is driven by the properties of the objects themselves. Some processes, such as motion or a sudden loud noise, can attract our attention in a pre-conscious, or non-volitional way. We attend to them whether we want to or not.
The second aspect is called top-down processing, also known as goal-driven, endogenous attention, attentional control or executive attention. This aspect of our attentional orienting is under the control of the person who is attending.
A related phenomenon is that of attentional shift. From Wikipedia:
Attentional shift (or shift of attention) occurs when directing attention to a point increases the efficiency of processing of that point and includes inhibition to decrease attentional resources to unwanted or irrelevant inputs. [...] Changes in spatial attention can occur with the eyes moving, overtly, or with the eyes remaining fixated, covertly. [...] Prior to an overt eye movement, where the eyes move to a target location, covert attention shifts to this location. However, it is important to keep in mind that attention is also able to shift covertly to objects, locations, or even thoughts while the eyes remain fixated.
A more specific focus is on visual attention control. From Wikipedia:
The spatial separation between two objects has an effect on attention. People can selectively pay attention to one of two objects in the same general location. Research has also been done on attention to non-object based things like motion. When directing attention to a feature like motion, neuronal activity increases in areas specific for the feature. [...] When people are told to look for motion, then motion will capture their attention, but attention is not captured by motion if they are told to look for color. [...] According to fMRI studies of the brain and behavioral observations, visual attention can be moved independently of moving eye position. Studies have had participants fixate their eyes on a central point and measured brain activity as stimuli were presented outside the visual fixation point. fMRI findings show changes in brain activity correlated with the shift in spatial attention to the various stimuli.
On the question of whether endogenous orienting of attention is an example of intentionality, I would argue yes, for the following reasons:
This type of focus is top-down, or executive in nature, hence being intentional.
Objects or parts of objects perceived presumably exist in both material and mental senses.
The experience has both content (mask, image, affect) and mode (vision).