We refer to a unique combination of input parameters, input images, output measures, and output images as a data record. As shown below, we combine a tabular visualisation of input parameters and output measures with an image browser for input and output images. We also describe design alternatives that we considered. We show the relationships between input parameters and output measures in a tabular visualisation see Figure 1 a.
Columns at the left represent parameters and columns at the right represent measures. Each data record is represented by a row that spans across the columns. The value taken for a parameter or measure is encoded in the corresponding column. If the vertical space per row is more than four pixels, a bar chart encodes every column, otherwise a line chart is used. Although line charts do not prevent over-plotting, they are effective to let users discern high-level patterns when limited vertical space is available.
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Visual parameter optimisation for biomedical image processing. The output images that are shown are the ones produced when the parameter values corresponding to the selected rows in the table are applied to the input images. The data shown here are from the case study and show results of a parameterised colour deconvolution technique applied to stained histology images of a liver section and lymphoma a type of blood cancer. Our objective, however, is to use the tabular representation to assist users in flexibly identifying and analysing relationships between parameters and measures. As we will show, we achieve this by extending our method with a number of interactive features.
Our method has an image browser at the right of the user interface. It shows a horizontal list of input images at the top see Figure 1 b. When users select rows in the tabular visualisation, the corresponding output images are shown below the input images in a grid Figure 1 c. Column i shows the output images produced by applying the algorithm to the i th input image. Each row represents a data record and the top-to-bottom order corresponds to the order of selected records in the tabular visualisation Figure 1 d.
By viewing the column of output images below each input image, users can compare output produced by different input parameter combinations for different input images. Each output image is blended with the input image to make comparisons easier the amount of blending is user-specified. Users can also define a rectangular region of interest in each input image to view for the output images.
This helps when there are particular regions that are known to be problematic for an algorithm see Figure 1 b and 1 c. Users can also adjust output image magnification. The primary mechanism to analyse relationships between input and output is interaction see Understanding , below. As an additional aid, we provide a summary where horizontal strips represent the domains of parameters and measures see Figure 1 e. Dark regions indicate the values to which currently displayed images correspond. We also considered alternative visualisation methods. Standard multidimensional visualisation methods were ruled out for the reasons below.
For dimensional stacking and hierarchical clustering, the real-estate requirements increase exponentially with the number of dimensions. Scatterplot matrices can visualise an arbitrary number of dimensions but, due to perceptual limitations, it is difficult to analyse relationships that span across more than two. For example, the multiway correlations that show up as nested patterns in Figure 1 a cannot be easily discerned in Figure 2 a , which shows the same data.
By contrast, parallel coordinates often mask such patterns when polylines overlay each other, requiring further interaction see Figure 2 b. To highlight cyclical patterns, we also considered spiral representations for example, [ 28 ].
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These require tuning an additional parameter to find a rotation interval and do not support multidimensional data. In fact, these alternatives all require far more effort for interacting with the data than our approach see Understanding , below. Alternative visualisations of the data shown in Figure 1. For both approaches, simple user interaction such as selection, is more complicated than with our method.
While developing our image browser we considered existing work for browsing photo libraries. Some, like PhotoFinder [ 29 ], show grids of sequentially ordered images. Others, like PhotoMesa [ 30 ], show the hard disk directory structure as a treemap.
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These methods were not designed to show relationships with and facilitate understudying of associated inputs and outputs. Users need to discover and analyse relationships between input and output. Interaction is key to flexibly select data records and inspect associated images.
For this, we combine column-based sorting, including automated sorting, with context-sensitive selection. Users can interactively sort the rows in the tabular visualisation to identify relationships, such as correlations, that span across input parameter and output measure space.
When users click on a column header, data records are sorted by the values of the corresponding input parameter or output measure. In Figure 3 a , the data have been sorted by the second parameter p 2. A step-like pattern has emerged where records are grouped into a number of bins with the same value for parameter p 2. It is possible to identify relationships between p 2 and some of the output measures at the right.
When multiple columns are selected, the order in which they were selected matters and all previously applied sortings are maintained. Figure 3 b shows the result of sorting Figure 3 a on p 1. The records are only reordered within each of the bins of p 2 to show a nested step-like pattern. Now, even more striking relationships with the output measures appear. Interactive sorting of input parameters of a colour deconvolution algorithm applied to a stained histology image of a liver section see case study. This yields a step-like pattern with a bin for each unique value that p 2 takes.
Also, correlations between p 2 and the output measures emerge, for example, p 2 is directly correlated with m 2 and inversely correlated with m 1 , m 3 , and m 6. For example, in addition to the direct correlation with p 2 , m 2 is also inversely correlated with p 1.
During prototyping, we repeatedly observed users searching for the parameter that most highly correlates with output measures. We consequently implemented a simple automated sorting facility that we call "smart sorting".
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The parameter with the highest correlation is identified and the data records are sorted by this parameter Figure 3 a. During prototyping, users found selection of individual data records too tedious to effectively analyse relationships between input and output.
To address this, we developed context-sensitive selection. Suppose the cursor intersects row r and column c. In addition to highlighting row r , all directly adjacent rows with the same value for column c also receive focus. For example, compare the highlighted rows in Figure 4 a , where the cursor intersects column one, to Figure 4 a where it intersects column two.
Rows in focus are enclosed by a red frame and marked by two red disks in the margins. Clicking selects all rows in focus and marks each selected record with blue disks. Compound selections are made by multiple selections of this type. Context-sensitive selection of the results in Figure 1 see case study.go
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When users move the cursor over the tabular visualisation, both the row and column that are intersected are considered. Clicking selects all rows that are in focus. Context-sensitive selection reduces effort to select multiple data records to display the corresponding output images in the image browser see Figure 1 d. Clicking on the button labelled "Show", below the tabular visualisation at the right, displays all images associated with selected data records in the image browser Figure 1 d.
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To provide more flexibility, users can rapidly filter records by clicking on "Filter" below any column and then specify an interval of interest. All records where the corresponding parameter or measure falls outside the interval are hidden. There are situations where users want to look at output images associated with a single data record in real time.
By holding the shift key, output images for the table row directly under the cursor are temporarily shown in the image browser. Images for a single record can be read and drawn at interactive speeds. We also investigated updating the image browser in real time as users select data records, or to use image caching. The former imposes a performance penalty for reading large numbers of images from disk, while the memory footprint of the latter limits scalability. Column sorting combined with context-sensitive selection is an effective and efficient way to investigate meaningful subsets of data.
We also considered "hard sorting" rows by column 1, then by column 2, and so on. This imposes a column-based hierarchy on the data and forces users to reorder columns to change the hierarchy. Instead, our approach lets users choose a column to sort on with one button click. For automated sorting, it is possible to rank all input parameters on their individual correlations and to sort the data by all parameters, in this rank order.
However, our users indicated that they prefer sorting by the single most significant parameter and our method therefore implements this approach. Providing automation as a "one-click" option, which can be visually verified and easily undone, alleviated fears about added complexity introduced by automated analysis. In this section, we describe applications of our method by providing an intuitive example and a case study.