Patent Publication Number: US-2018032816-A1

Title: Fixation identification using density optimization

Description:
RELATED APPLICATIONS 
     This patent application claims the benefit of U.S. Provisional Application No. 62/368,992, filed on Jul. 29, 2016, entitled, “Fixation Identification Using Density Optimization,” the contents and teachings of which are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     Many complex tasks involve the use of visual displays, such as computer displays. Individuals using these displays are required to make efficient visual searches of their screens to review and/or locate pertinent information. To evaluate an individual&#39;s performance as well as a display&#39;s usefulness, it is considered desirable to know precisely where and for long an individual looks at the display during critical times. In addition, in assessing the effectiveness of any visual display, it is useful to know not only what features of the display an individual focuses on, but whether cognitive activity occurs. 
     Eye-tracking provides a metric that can measure what a user read/viewed on the display and can identify cognitive processing associated with the viewing. Conventional eye-tracking devices are configured to record eye-tracking, or gaze, data of a subject that is presented a visual stimulus and to perform fixation identification associated with the eye-tracking data. Fixation identification separates eye-tracking data into fixations and saccades. Fixations identify pauses over regions of interest of the visual display, such as where cognitive processing is believed to occur. Saccades relate to relatively rapid movements of a user&#39;s eye between fixations. 
     Conventional eye-tracking devices can be further configured to utilize different methods to analyze and process eye-tracking data. One method involves the use of gaze-point position (e.g., I-DT filtering). With I-DT filtering, the eye-tracking device is configured to separate eye-tracking data as either fixations or saccades using a predefined maximum dispersion threshold together with a minimum duration value. For example, the eye-tracking device can utilize a fixed-area window to identify fixations by sequentially adding points beyond a minimum duration until the dispersion threshold is exceeded. 
     Another method to analyze and process the eye-tracking data involves the use of gaze-point velocity (e.g., I-VT filtering). With I-VT filtering, the eye-tracking device is configured to sequentially categorize each gaze point based on its point-to-point velocity. If the velocity associated with a gaze point meets or exceeds a velocity threshold, the eye-tracking device can characterize the gaze point as a saccade. However, if the velocity associated with a gaze point is below the velocity threshold, the eye-tracking device can characterize the gaze point as a fixation. 
     SUMMARY 
     Conventional eye-tracking devices can suffer from a variety of deficiencies. For example, as provided above, conventional eye tracking can be utilized to detect items that a user has viewed, such as on a display screen. The resulting eye-tracking data, or gaze data, can be categorized into two main events or categories: fixations which represent focused eye movement, indicative of awareness and attention, and saccades which represent relatively higher velocity movements that occur between fixation events. 
     Primary existing methods for identifying fixations use either gaze location (e.g., I-DT filter) or velocity metrics (e.g., I-VT filter). Methods based on gaze location (e.g., I-DT filter) use a constant area size as the threshold for grouping consecutive gaze points into a fixation, while methods based on velocity metrics (e.g., I-VT filter) use a fixed velocity threshold to separate fixations from saccades. While these existing approaches are relatively simple to implement and generally effective, they can lead to issues with precision because they are prone to including points on the fringe of tolerance settings. Because the data generated can lack sensitivity to peripheral points, the use of existing approaches can misrepresent positional and durational properties of fixations and skew summary fixation metrics. 
     By contrast to conventional methods for comprehension of information from visual information sources, embodiments of the present innovation relate to fixation identification using density optimization. In one arrangement, a fixation identification device is configured to receive gaze position data, such as an (x, y) Cartesian coordinate data element along with associated time information, from an eye tracking device. With this data, the fixation identification device can identify a user&#39;s eye position relative to a field of view, such as a display, at a corresponding time. The fixation identification device is configured to identify the gaze position data as either fixation gaze position data or saccade gaze position data and to cluster the fixation gaze position data into successive fixation regions or chunks. The fixation identification device is configured to then identify the densest fixations within a given fixation region using various optimization formulations. In one arrangement, the fixation identification device can utilize a user-selected density adjustment parameter that adjusts the degree of desired density for the fixation regions, thereby allowing decision makers to have fine-tuned control over density during the process. 
     Based upon the user&#39;s eye movement data, and specifically the density of fixation information or optimized fixation density, the adaptive decision support device is configured to detect the user&#39;s relative levels of cognitive effort or load. For example, the fixation identification device is configured to utilize the user&#39;s density of fixation information to predict the user&#39;s activity. In one arrangement, the fixation identification device can utilize the user&#39;s density of fixation information to assess the user&#39;s visual engagement of an item (e.g., whether a user visually searched for particular information or read a piece of text) and to provide output based upon the assessment. 
     By detecting the user&#39;s cognitive load through changes in the density optimized fixation data, the fixation identification device is configured to provide recommendations for the use of decision models that are best at optimizing the effort-accuracy tradeoff at the detected level of cognitive load. Further, based upon the assessment of the user&#39;s visual engagement of an item, the fixation identification device is configured to provide feedback information to an operator regarding the user&#39;s visual engagement of an item (e.g., suggestions as to improvements of the design or layout of the item or suggestions to improve the needs of the user). Accordingly, the fixation identification device can serve as a tool in personalizing decision support training. 
     In one arrangement, a fixation identification device includes a controller having a memory and a processor. The controller is configured to identify each gaze position data element received from an eye-tracking device as one of fixation gaze position data and saccade gaze position data, each gaze position data element corresponding to a visual location associated with a field of view at a corresponding time and identify at least one fixation region associated with the fixation gaze position data. The controller is configured to adjust a number of fixation gaze position data elements associated with the at least one fixation region and generate a density optimized fixation region based upon the adjusted number of fixation gaze position data elements. 
     In one arrangement, a fixation identification system includes an eye-tracking device and a fixation identification device disposed in electrical communication with the eye-tracking device. The fixation identification device includes a controller having a memory and a processor, the controller being configured to identify each gaze position data element received from the eye-tracking device as one of fixation gaze position data and saccade gaze position data, each gaze position data element corresponding to a visual location associated with a field of view at a corresponding time; identify at least one fixation region associated with the fixation gaze position data; adjust a number of fixation gaze position data elements associated with the at least one fixation region; and generate a density optimized fixation region based upon the adjusted number of fixation gaze position data elements. 
     In one arrangement, in a fixation identification device, a method for optimizing visual engagement of a field of view, comprising identifying, by the fixation identification device, each gaze position data element received from an eye-tracking device as one of fixation gaze position data and saccade gaze position data, each gaze position data element corresponding to a visual location associated with a field of view at a corresponding time; identifying, by the fixation identification device, at least one fixation region associated with the fixation gaze position data; adjusting, by the fixation identification device, a number of fixation gaze position data elements associated with the at least one fixation region; and generating, by the fixation identification device, a density optimized fixation region based upon the adjusted number of fixation gaze position data elements. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features and advantages will be apparent from the following description of particular embodiments of the innovation, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of various embodiments of the innovation. 
         FIG. 1  illustrates a block diagram of a fixation identification system, according to one arrangement. 
         FIG. 2  illustrates a flow chart of a procedure performed by the fixation identification device of  FIG. 1 , according to one arrangement. 
         FIG. 3  illustrates an image provided by a display of  FIG. 1  and gaze position data elements associated with the image, according to one arrangement. 
         FIG. 4  illustrates the image of  FIG. 3 , identifying fixation regions associated with the gaze position data, according to one arrangement. 
         FIG. 5  illustrates a block diagram of a fixation identification system, according to one arrangement. 
         FIG. 6A  illustrates application of a formulation to fixation gaze position data elements, according to one arrangement. 
         FIG. 6B  illustrates application of a formulation to fixation gaze position data elements, according to one arrangement. 
         FIG. 7  illustrates the image of  FIG. 4 , identifying density optimized fixation regions associated with an image, according to one arrangement. 
         FIG. 8A  illustrates application of a formulation to fixation gaze position data elements, according to one arrangement. 
         FIG. 8B  illustrates application of a formulation to fixation gaze position data elements, according to one arrangement. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present innovation relate to fixation identification using density optimization. In one arrangement, a fixation identification device is configured to receive gaze position data, such as an (x, y) Cartesian coordinate data element along with associated time information, from an eye tracking device. With this data, the fixation identification device can identify a user&#39;s eye position relative to a field of view, such as a display, at a corresponding time. The fixation identification device is configured to identify the gaze position data as either fixation gaze position data or saccade gaze position data and to cluster the fixation gaze position data into successive fixation regions or chunks. The fixation identification device is configured to then identify the densest fixations within a given fixation region using various optimization formulations. In one arrangement, the fixation identification device can utilize a user-selected density adjustment parameter that adjusts the degree of desired density, thereby allowing decision makers to have fine-tuned control over density during the process. 
     Based upon the user&#39;s eye movement data, and specifically the density of fixation information or optimized fixation density, the adaptive decision support device is configured to detect the user&#39;s relative levels of cognitive effort or load. For example, the fixation identification device is configured to utilize the user&#39;s density of fixation information to predict the user&#39;s activity. In one arrangement, the fixation identification device can utilize the user&#39;s density of fixation information to assess the user&#39;s visual engagement of an item (e.g., whether a user visually searched for particular information or read a piece of text) and to provide output based upon the assessment. 
       FIG. 1  illustrates a schematic representation of a fixation identification system  10 , according to one arrangement. As illustrated, the fixation identification system  10  includes an eye-tracking device  12  disposed in electrical communication with a fixation identification device  14 . 
     The eye-tracking device  12  is configured to detect the position of a user&#39;s eye relative to a field of view, such as a display  16  or any image received by the user, whether generated electronically or otherwise, based upon the measured position of the user&#39;s eye in space. For example, the eye-tracking device  12  can include an infra-red (IR) transmitter  22  and camera  24  disposed in electrical communication with a controller  25 , such as a processor and a memory. The transmitter  22  is configured to direct a light  18 , such as an infrared (IR) light, against a user&#39;s eye  20 . The light  18  allows the camera  24  of the eye-tracking device  12  to identify the pupil of the eye and creates a glint on the surface of the eye  20 . The position of the glint relative to the eye-tracking device  12  is substantially stationary. Accordingly, as the user&#39;s eye and pupil moves to identify and track various items, such as provided on the display  16 , the glint acts as a reference point for the camera  24 . 
     The fixation identification device  14  is configured as a computerized device, such as a personal computer, laptop, or tablet and can include a controller  28 , such as a processor and a memory. During operation, as will be described in detail below, the fixation identification device  14  is configured to receive gaze position data elements  26  from the eye-tracking device  12  and to identify user gaze fixation regions utilizing a density optimization approach. For example, the fixation identification device  14  can include a density optimizer  70  configured to optimize a density value associated with a fixation region, such as a region viewed by a user in a field of view. Relatively dense gaze fixation regions identify a more focused visual attention by a user. By utilizing density optimization, rather than solely distance or velocity as is conventionally utilized, the fixation identification device  14  can identify the spatial concentration of gaze points and can correlate the relatively dense concentrations with a user&#39;s focus. Based upon the focus, the fixation identification device  14  can provide feedback to the user, such as suggestions regarding optimizing the user&#39;s interaction with the field of view. 
     In one arrangement, each of the eye-tracking device  12  and the fixation identification device  14  are configured as standalone devices disposed in electrical communication with each other. In one arrangement, the fixation identification system  10  includes both the eye-tracking device  12  and the fixation identification device  14  as part of a single device. 
     The controller  28  of the fixation identification device  14  can store an application for optimizing the density of user gaze fixations. The optimization application installs on the controller  28  from a computer program product  30 . In some arrangements, the computer program product  30  is available in a standard off-the-shelf form such as a shrink wrap package (e.g., CD-ROMs, diskettes, tapes, etc.). In other arrangements, the computer program product  30  is available in a different form, such downloadable online media. When performed on the controller  28  of the fixation identification device  14 , the optimization application causes the fixation identification device  14  to detect the density of identified fixation regions associated with a user&#39;s field of view, such as the view of the display  16 . Based upon the detected densities, the optimization application causes the fixation identification device  14  to provide feedback to the user to improve the user&#39;s visual interaction with the field of view. 
       FIG. 2  illustrates a flow chart  100  of a procedure performed by the fixation identification device  14  of the fixation identification system  10  of  FIG. 1  when providing fixation identification using density optimization. 
     In element  102 , the fixation identification device  14  is configured to identify each gaze position data element received from the eye-tracking device  12  as one of fixation gaze position data and saccade gaze position data, each gaze position data element corresponding to a visual location associated with a field of view at a corresponding time. 
     For example, with reference to  FIG. 1 , as a user visually focuses on a field of view, such as the display  16 , the eye-tracking device  12  detects user&#39;s eye position in three dimensions (x, y, z) of the user&#39;s pupil when viewing a location  22  in a field of view, such as a display  16 , and projects the user&#39;s eye position into two dimensions (x, y in another coordinate system), so that the two-dimensional coordinate represents where the user is looking in a field of view, such as on the display  16 . Based upon the detected positioning of the pupil relative to the glint, the eye-tracking device  12  provides a vertical and lateral coordinate (x, y), termed a gaze position data element  26  herein, to the fixation identification device  14 . For example, the gaze position data element  26  corresponds to the user&#39;s visual focus on the location  22  on the display  16 . Further, for each gaze position data element  26 , the controller  24  also collects an associated time measurement (t). For example, the eye-tracking device  24  can be configured to collect gaze position data elements  26  at a rate between about 10 Hz and 1250 Hz. Assuming the case where the eye-tracking device  12  collects data at a rate of 30 Hz, for each gaze position data element collected, the eye-tracking device  12  associates a corresponding time of 1/30 second. 
     After receiving the gaze position data elements  26 , the fixation identification device  14  can identify the user&#39;s eye position relative to the field of view. For example, with reference to  FIG. 3 , based upon the gaze position data elements  26  received from the eye-tracking device  12 , the fixation identification device  14  can identify the position of the user&#39;s eyes relative to an image  32 , such as a website, provided by the display  16 . 
     Returning to  FIG. 1 , in order to detect the user&#39;s relative levels of cognitive effort associated with the viewing of the display  16 , the fixation identification device  14  is configured to translate the gaze position data elements  26  into distinct eye-movement, or oculomotorevents. For example, the fixation identification device  14  is configured to separate the gaze position data elements  26  into either fixation gaze position data  44  or saccade gaze position data  46 . Fixation gaze position data  44 , or fixations, identify pauses over informative regions of interest, where cognitive processing is believed to occur. Fixations characterize attention because they represent effort in maintaining a relatively stable gaze to take foveal snapshots of an object for subsequent processing by the brain. By contrast, saccade gaze position data  46 , or saccades, identify relatively rapid movements between fixations, used to recenter the eye on a new location. By identifying certain gaze position data elements  26  as fixation gaze position data, the fixation identification device  14  is configured to detect image regions on which a user has focused his attention and has performed a level of cognitive processing. 
     The fixation identification device  14  can be configured to separate the gaze position data elements  26  into either fixation gaze position data  44  or saccade gaze position data  46  in a variety of ways. In one arrangement, the fixation identification device  14  distinguish the gaze position data elements  26  based upon the relative angular velocity  40  between consecutive gaze position data elements  26 , as provided below. 
     For example, with additional reference to  FIG. 3 , assume the case where the fixation identification device  14  receive a first gaze position data element  26 - 1  which identifies a first visual location (x 1 , y 1 ) of the field of view at an associated first time (t 1 ). Further, assume the case where the fixation identification device  14  receive a second gaze position data element  26 - 2 , subsequent and consecutive to the first gaze position data element  26 - 1 , which identifies a second visual location (x 2 , y 2 ) of the field of view at an associated second time (t 2 ). 
     With the information from the first and second gaze position data elements  26 - 1 ,  26 - 2  and using the position of the glint created by the eye tracking device  12  on the user&#39;s eye as the origin, the fixation identification device  14  can detect an angular velocity  40  of the second gaze position data  26 - 2  relative to the first gaze position data  26 - 1 . With the angular velocity  40  detected, the fixation identification device  14  compares the angular velocity  40  with a velocity threshold value  42  to determine if the second gaze position data  26 - 2  represents a fixation or a saccade. While the velocity threshold value  42  can have a variety of values, in one arrangement, the velocity threshold value  42  is equal to an angular velocity value of 30°/second. 
     Based upon the comparison, when the relative angular velocity  40  associated with the second gaze position data  26 - 2  relative to the first gaze position data  26 - 1  is below the velocity threshold value  42 , the fixation identification device  14  identifies the second visual location associated with the second gaze position data  26 - 2  as fixation gaze position data  44 . Alternately, when the relative angular velocity  40  associated with the second gaze position data  26 - 2  relative to the first gaze position data  26 - 1  meets or exceeds the velocity threshold value  42 , the fixation identification device  14  identifies the second visual location associated with the second gaze position data  26 - 2  as saccade gaze position data  46 . 
     Further, the fixation identification device  14  is configured to continue to receive subsequent gaze position data elements  26 -N and to analyze these subsequent data elements  26 -N to detect the gaze position data elements  26  received from the eye-tracking device  12  as either a fixation gaze position or saccade gaze position in a substantially continuous manner. For example, with additional reference to  FIG. 3 , for each subsequent gaze position data element  26 -N received, the fixation identification device  14  detects the angular velocity  40  of the subsequent gaze position data element  26 -N relative to the previous gaze position data element, in this case data element  26 - 2 , and compares the angular velocity  40  with the threshold value  42 . Based upon the results of the comparison the fixation identification device  14  can identify the subsequent gaze position data elements  26 -N as fixation gaze position data  44  or saccade gaze position data  46 . Accordingly, the fixation identification device  14  is configured to provide real time analysis of the gaze position data elements  26  during operation. 
     Returning to  FIG. 2 , as indicated in element  104 , as the fixation identification device  14  receives the gaze position data elements  26  and identifies certain data elements  26  as fixation gaze position data elements  44 , the fixation identification device  14  is configured to identify at least one fixation region  50  associated with the fixation gaze position data  44 . During operation, and with additional reference to  FIGS. 4 and 5 , as the fixation identification device  14  identifies gaze position data elements  26  as fixation gaze position data elements  44 , the fixation identification device  14  groups these fixation gaze position data elements  44  into chunks or fixation regions  50 . In one arrangement, the fixation identification device  14  includes certain fixation gaze position data elements  44  as part of a given region  50  based upon the fixation gaze position data elements  44  being consecutive in time and having a particular duration. 
     For example, during operation and with reference to  FIG. 5 , the fixation identification device  14  is configured to identify a received number of consecutive gaze position data elements  26  as fixation gaze position data  44 . Assume the case where the fixation identification device  14  receives gaze position data elements  26 - 1  through  26 - 4 . To detect if the gaze position data elements  26 - 1  through  26 - 4  are consecutive to each other, the fixation identification device  14  can identify the time measurements (t 1 ), (t 2 ), (t 3 ), and (t 4 ) of the gaze position data elements  26 - 1  through  26 - 4  and can detect if t 4 &gt;t 3 &gt;t 2 &gt;t 1 . Following identification of the gaze position data elements  26 - 1  through  26 - 4  as being consecutive, the fixation identification device  14  can identify the gaze position data elements  26 - 2  through  26 - 4  as being fixation gaze position data elements  44 - 2  through  44 - 4  by detecting the relative angular velocity  40  of the elements and comparing to the threshold value  42 . 
     Further, to determine if the data elements  44 - 2  through  44 - 4  belong to a single fixation region  50 , the fixation identification device  14  is configured to identify a separation event associated with the gaze position data elements  26  received from the eye-tracking device  12 . For example, during a gaze sequence, the receipt of a saccade gaze position data element  46  can identify the separation of groupings of fixation gaze position data elements  44 . Accordingly, following the receipt of a set of fixation gaze position data elements, in the case where the fixation identification device  14  identifies a received gaze position data element  26  as a saccade gaze position data element  46 - 5  the fixation identification device  14  can review the consecutive fixation gaze position data elements  44 - 2  through  44 - 4  for duration. 
     In one arrangement, the fixation identification device  14  can compare duration value  60 - 2  through  60 - 4  associated with each of the fixation gaze position data elements  44 - 2  through  44 - 4  and compare the duration values  60 - 2  through  60 - 4  with a duration threshold  62 , such as a threshold of at least 100 ms. For example, the duration values  60 - 2  through  60 - 4  can identify an amount of time that a user viewed a particular gaze position of a field of view. To determine the duration values  60 - 2  through  60 - 4 , the fixation identification device  14  is configured to take the difference between a time measurement (t) associated with a given fixation gaze position data element  44  and a time measurement (t) associated with a previous consecutive fixation gaze position data element  44 . 
     In the case when fixation identification device  14  identifies the duration values  60 - 2  through  60 - 4  of consecutive fixation gaze position data elements  44 - 2  through  44 - 4  as meeting the duration threshold  62 , the fixation identification device  14  can identify the fixation gaze position data elements  44 - 2  through  44 - 4  as belonging to a given fixation region  50 . For example, with reference to  FIG. 4 , in the case where the consecutive fixation gaze position data elements  44 - 2  through  44 - 4  have a duration that is at least 100 ms, the fixation identification device  14  identifies the fixation gaze position data elements  44 - 2  through  44 - 4  as being part of the fixation region  50 - 1 . 
     By grouping particular fixation gaze position data elements  44  with associated fixation regions  50 , each fixation region  50  has a particular density, based upon the boundaries of the region  50  and the number of fixation gaze position data elements  44  included in the boundary. 
     In one arrangement, with reference to  FIG. 4 , each fixation region  50 , such as fixation region  50 - 2 , is defined by a boundary  64  based upon maximum and minimum x-coordinate and y-coordinate values (x, y) associated with the fixation gaze position data  44 . For example, the boundary  64  can define a square about the fixation gaze position data  44  such that the maximum y-value of the fixation gaze position data  44  defines the top boundary, the minimum y-value of the fixation gaze position data  44  defines the bottom boundary, the maximum x-value of the fixation gaze position data  44  defines a first side boundary, and the minimum x-value of the fixation gaze position data  44  defines the second side boundary. The density of the fixation region  50 - 2  is defined as a ratio between the number of fixation gaze position data elements  44  associated with the at least one fixation region  50 - 2  and an area defined by the boundary  64  of the at least one fixation region  50 - 2 . 
     It is important to note that the density value associated with the fixation region  50  is distinct from the seemingly similar, but separate, conventional notion of spatial density, which addresses the concept of the proximity of multiple clusters of gaze points (i.e., fixation gaze position data elements). Spatial density involves the post-processing of merging individual fixations into a larger fixation, as performed on a fixation density map, for example. Further, in one arrangement and for multiple fixation regions  50  identified, the fixation identification device  14  is configured to identify the density of a single fixation region  50  at a time. 
     As provided above, relatively dense gaze fixation regions identify a more focused visual attention by a user. While each fixation region  50  defines a corresponding density, the fixation identification device  14  is further configured to identify the densest fixations within a given fixation region  50 . Accordingly, returning to  FIG. 2 , in element  106 , the fixation identification device  14  is configured to adjust a number of fixation gaze position data elements  44  associated with the at least one fixation region  50 . Further, in element  108 , the fixation identification device  14  is configured to generate a density optimized fixation region  80  based upon the adjusted number of fixation gaze position data elements 
     When executing elements  106  and  108 , with additional reference to  FIG. 1 , the fixation identification device  14  can utilize the density optimizer  70  to apply an optimization function  74  to the fixation gaze position data elements  44  of each fixation region  50 . The optimization function  74  can be configured in a variety of ways. Examples of various optimization function configurations are provided below. 
     In one arrangement, the optimization function  74  is configured to minimize the number of fixation gaze position data elements  44  associated with a given fixation region  50 . For example, utilizing the optimization function  74 , the fixation identification device  14  selects a fixation gaze position data element  44  to be included as part of a density optimized fixation region when it improves a density-based metric. Accordingly, the optimization function  74  can be configured to apply the following formulation to the fixation gaze position data elements  44  associated with a given fixation region  50 : 
     
       
         
           
             
               
                 
                   
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     Formulation (1) uses values d ij  as the Euclidean distances between two fixation gaze position data elements  44 , i and j, i&lt;j. 
       FIG. 6A  illustrates the application of the formulation (1) to the fixation gaze position data elements  44  by the fixation identification device  14 . For each fixation gaze position data element  144 - 1  through  144 - 5  associated with the fixation region  150 , the fixation identification device  14  detects a distance D between that a fixation gaze position data element and every other fixation gaze position data element associated with the fixation region  150 . For example, with elements  144 - 1  through  144 - 5  in the fixation region  150 , the fixation identification device  14  computes the distances D using the Euclidean distance between position (x, y) of a first element and position (x, y) of a second element. For the example, as provided in  FIG. 6A , the fixation identification device  14  detects the nine distances between each fixation gaze position data element pair. 
     Next, the fixation identification device  14  is configured to detect various combinations  160  of fixation gaze position data element  144 . For example, the fixation identification device  14  can detect elements  144 - 1   144 - 2 , and  144 - 3  as part of a first combination of fixation gaze position data elements  160 - 1  and can detect elements  144 - 1 ,  144 - 2 , and  144 - 5  as part of a second combination of fixation gaze position data elements  160 - 2 . 
     For each combination  160 , the fixation identification device  14  determines if the fixation gaze position data elements  144  within the combination  160  meet a duration threshold  62  (e.g., at least 100 ms) and are consecutive to each other (e.g., t 4 &gt;t 3 &gt;t 2 &gt;t 1 ). If the fixation gaze position data elements  144  within the combination  160  meet those criteria, the fixation identification device  14  is configured to apply the first term of the formulation (1) to detect a density of the combination of fixation gaze position data elements  160  based upon a ratio of the detected distances (D) of the combination of fixation gaze position data elements and a count of fixation gaze position data elements associated with the combination (z). 
     After having detected the density for each qualifying combination of fixation gaze position data elements  160 , the fixation identification device  14  is configured to identify the combination  160  having the greatest detected density. Once detected, as indicated in  FIGS. 6A and 7 , the fixation identification device  14  utilize the fixation gaze position data elements  144  of that densest combination to define the density optimized fixation region  80 . 
     In one arrangement, with reference to  FIG. 6B , the fixation identification device  14  is configured to utilize a density adjustment parameter  75  to adjust the degree of desired density for a given fixation region  50 . The density adjustment parameter  75  balances a tradeoff between the inclusion of additional fixation gaze position data elements  144  and the spatial concentration of fixation gaze position data elements  144  within a density optimized fixation region  80 . The parameter  75  can be configured as a user-selected parameter  75  which allows an end user to discriminate the number of fixation gaze position data elements  144  associated with the fixation region  50  and have fine-tuned control over the density and the resulting density optimized fixation region  80  during operation. 
     In one arrangement, the formulation (1) can include a second term, as provided below: 
     
       
         
           
             
               
                 
                   
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                                 = 
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                               tf 
                             
                           
                         
                         + 
                         
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                               ( 
                               
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                     . 
                   
                 
               
               
                 
                   ( 
                   2 
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     With reference to the formulation (2), the parameter (a) in the second term of the formulation represents the density adjustment parameter  75 . The lower the value of the density adjustment parameter  75 , the lower the number of additional fixation gaze position data elements  144  included within the density of a combination of fixation gaze position data elements  160 . By contrast, the greater the value of the density adjustment parameter  75 , the larger the number of additional fixation gaze position data elements  144  included within the density of a combination of fixation gaze position data elements  160 . For example, when applying both the first term and the second term of formulation (2), as indicated in  FIG. 6B , application of the density adjustment parameter  75  to the fixation gaze position data elements  144  associated with the fixation region  150  results in a greater number of fixation gaze position data elements  144 - 1  through  144 - 4  included as part of the density optimized fixation region  80 . 
     In one arrangement, the optimization function  74  is configured to minimize the square area associated with a given fixation region  50 . For example, the optimization function  74  can be configured to apply the following formulation to the fixation gaze position data elements  44  associated with a given fixation region  50 : 
     
       
         
           
             
               
                 
                   
                     ∑ 
                     
                       f 
                       = 
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                     F 
                   
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                       [ 
                       
                         r 
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                     . 
                   
                 
               
               
                 
                   ( 
                   3 
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     The formulation (3) balances defining a boundary around the largest number of fixation gaze position data elements  44  with a two-dimensional square of minimal area, as measured by half of the side length r. 
       FIG. 8A  illustrates the application of the first term of the formulation (3) to the fixation gaze position data elements  44  by the fixation identification device  14 . During operation, the fixation identification device  14  selects a fixation center  165  of the fixation region  150  associated with the fixation gaze position data elements  144 . The fixation identification device  14  then defines a minimized boundary length r of a fixation center boundary  167  of the fixation region  150  from the selected fixation center  165 . When defining, or adding, the minimized boundary length r to the fixation center  165 , the fixation identification device  14  sets the corresponding square fixation center boundary  167  with each side having a length  2   r.    
     As the fixation identification device  14  adjusts the position of the fixation center  165  or the boundary length r, the fixation identification device  14  determines if the fixation gaze position data elements  144  within the fixation center boundary  167  meet a duration threshold  62  (e.g., at least 100 ms) and are consecutive to each other (e.g., t 4 &gt;t 3 &gt;t 2 &gt;t 1 ). If the fixation gaze position data elements  144  within the fixation center boundary  167  meet those criteria, the fixation identification device  14  is configured to identify the fixation center boundary  167  as the density optimized fixation region  80 . 
     In one arrangement, the formulation (3) can include a second term, as provided below: 
     
       
         
           
             
               
                 
                   
                     ∑ 
                     
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                       = 
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                       [ 
                       
                         
                           r 
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                         + 
                         
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                               ( 
                               
                                 1 
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                       ] 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     With reference to the formulation (4), the parameter (a) in the second term of the formulation represents a density adjustment parameter  75 . In one arrangement, the fixation identification device  14  is configured to utilize the density adjustment parameter  75  to adjust the degree of desired density for a given fixation region  50 . With reference to the formulation (2), the parameter (a) in the second term of the formulation represents the density adjustment parameter  75 . The lower the value of the density adjustment parameter  75 , the lower the number of additional fixation gaze position data elements  144  included within the density of a combination of fixation gaze position data elements  160 . By contrast, the greater the value of the density adjustment parameter  75 , the larger the number of additional fixation gaze position data elements  144  included within the density of a combination of fixation gaze position data elements  160 . For example, when applying both the first term and the second term of formulation (4), as indicated in  FIG. 8B , application of the density adjustment parameter  75  to the fixation gaze position data elements  144  associated with the fixation region  150  results in a greater number of fixation gaze position data elements  144 - 1  through  144 - 4  included as part of the density optimized fixation region  80 . 
     As provided above, the density optimized fixation region  80  provides insight into a user&#39;s associated cognitive load and engagement of a field of view, such as a display  16 . Based upon the correlation between the density optimized fixation region  80  and a user&#39;s cognitive load and engagement, and with reference to  FIG. 1 , the fixation identification device  14  is configured to provide feedback information  200  to the user, such as via display  16 . For example, the feedback information  200  can provide recommendations for the use of decision models that can optimize the effort-accuracy tradeoff at the detected level of cognitive load, as based upon the density optimized fixation region  80 . 
     Further, based upon a correlation of the density optimized fixation region  80  with a user behavior criterion  202 , the feedback information  200  can include information regarding the user&#39;s visual engagement of an item (e.g., suggestions as to improvements of the design or layout of the image  32 , such as a website, provided by the display  16  or suggestions to improve the needs of the user). Accordingly, the fixation identification device  14  can serve as a tool in personalizing decision support training. 
     The fixation identification device  14  is configured identify density optimized fixation regions  80  based on how densely the fixation gaze position data elements  44  are packed. This is different from the use of IDT (fixed window) and IVT (velocity) in conventional system. By contrast, embodiments of the fixation identification device  14  optimizes the density of an identified fixation region to provide more accurate informative than conventionally detected. 
     Further, as provided above, the fixation identification device  14  is configured to identify fixation regions  50  associated with the field of view and optimize the density of those regions to accurately detect a user&#39;s relative levels of cognitive effort associated with the viewing of a field of view. With the configuration described, the fixation identification device  14  can provide such detection and optimization in substantially real time. Accordingly, the feedback provided to the user can also be provided in substantially real time, such as in order to redirect the user&#39;s attention to a particular location in the field of view. 
     Additionally, by optimizing the density of fixation regions  50 , the fixation identification device  14  reduces the computation time needed to identify fixations across a field of view. For example, a user&#39;s gaze sequence typically contains a relaively large number of (x, y) coordinats over time. Typical lengths of gaze data sequences are in the tens to hundreds of seconds. For frequencies of 10 Hz to 1250 Hz, the user&#39;s gaze sequence can contain between about several hundred to hundreds of thousands of gaze position data elements and may contain thousands of fixation gaze position data elements. For such data instances, fixation region identification can be computationally demanding. By optimizing the density of fixation regions  50 , the fixation identification device  14  reduces such computational demand. 
     Further, the fixation identification device  14  is configured to detect fixation gaze position data based upon optimized density of the fixation regions, as opposed to solely distance (I-DT) or velocity (I-VT), as is performed by conventional devices. By optimizing the density of the fixation regions, the fixation identification device  14  can correlate the resulting density values with two characterizations of cognitive effort: the duration of a fixation, as well as the proximal compactness of the fixations. Fixation duration is a reliable measure of attention and proximal compactness of individual gaze points in a fixation represent a user&#39;s focused attention and increased levels of information processing. Accordingly, fixation regions with greater density values tend to exclude peripheral gaze points, thereby improving the accuracy of traditional fixation metrics. 
     While various embodiments of the innovation have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the innovation as defined by the appended claims.