The handwriter package performs writership analysis of a handwritten questioned document where the questioned document was written by one of closed-set of potential writers. For example, a handwritten bomb threat is found in a science classroom, and the police are able to determine that the note could only have been written by one of the students in 4th period science. The handwriter package builds a statistical model to estimate a writer profile from known handwriting samples from each writer in the closed-set. A writer profile is also estimated from the questioned document. The statistical model compares the writer profile from the questioned document with each of the writer profiles from the closed-set of potential writers and estimates the posterior probability that each closed-set writer wrote the questioned document.
You can install handwriter from CRAN with:
You can install the development version of handwriter from GitHub with:
The file “phrase_example.png” is a scanned PNG of handwriting from the CSAFE Handwriting Database. This PNG image is included in the handwriter package in a folder called “extdata.” Use the helper function handwriter_example() to find the path to where “phrase_example.png” is saved on your computer.
Use processDocument() to
library(handwriter)
phrase <- system.file("extdata", "phrase_example.png", package = "handwriter")
doc <- processDocument(phrase)
#> path in readPNGBinary: /private/var/folders/1z/jk9bqhdd06j1fxx0_xm2jj980000gn/T/RtmpEaTBth/temp_libpath12a739c097f/handwriter/extdata/phrase_example.png
#> Starting Processing...
#> Getting Nodes...and merging them...
#> Finding direct paths...and loops...
#> Looking for graph break points...and discarding bad ones...
#> Isolating graph paths...
#> Organizing letters...
#> Creating letter lists...
#> Adding character features...
#> Document processing complete.We can view the image:
We can view the thinned image:
We can also view the nodes:
This section explains how to perform handwriting analysis on questioned documents using handwriter. In particular, handwriter addresses the scenario where an investigator has a questioned handwritten document, a group of persons of interest has been identified, and the questioned document had to have been written by one of the persons of interest. For example, imagine that a handwritten bomb threat was left at a office building’s main desk and the police discover that the note had to have been written by one of the one hundred employees working that day. More details on this method can be found in [Crawford 2022].
Create a new folder called main_dir on your computer to hold the handwriting documents to be analyzed. When we create a new clustering template and fit a statistical model, those files will also be stored in this folder. Create a sub-folder in main_dir called data. In the data folder, create sub-folders called model_docs, questioned_docs, and template_docs. The folder structure will look like this:
Save the handwritten documents that you want to use to train a new cluster template as PNG images in main_dir > data > template_docs. The template training documents need to be from writers that are NOT people of interest. Name all of the PNG images with a consistent format that includes an ID for the writer. For example, the PNG images could be named “writer0001.png”, “writer0002.png”, “writer0003.png” and so on.
Next, create a new cluster template from the documents in main_dir > data > template_docs with the function make_clustering_templates. This function
template_docs, decomposing the handwriting into component shapes called graphs. The processed graphs are saved in RDS files in main_dir \> data \> template_graphs.max_edges.K starting cluster centers using seed centers_seed for reproducibility.K starting cluster centers and the selected graphs. The algorithm iteratively groups the selected graphs into K clusters. The final grouping of K clusters is the cluster template.writer_indices is a vector of the start and stop characters of the writer ID in the PNG image file name. For example, if the PNG images are named “writer0001.png”, “writer0002.png”, “writer0003.png”, and so on, writer_indices = c(7,10)num_dist_cores.template <- make_clustering_templates(
template_dir = "path/to/main_dir",
template_images_dir = "path/to/main_dir/data/template_docs",
writer_indices = c(7,10),
max_edges = 25,
centers_seed = 100,
graphs_seed = 101,
K = 40,
num_dist_cores = 4,
max_iters = 25)Type ?make_clustering_templates in the RStudio console for more information about the function’s arguments.
For the remainder of this tutorial, we use a small example cluster template, example_cluster_template included in handwriter.
The idea behind the cluster template and the hierarchical model is that we can decompose a handwritten document into component graphs, assign each graph to the nearest cluster, the cluster with the closest shape, in the cluster template, and count the number of graphs in each cluster. We characterize writers by the number of a writer’s graphs that are assigned to each cluster. We refer to this as a writer’s cluster fill counts and it serves as writer profile.
We can plot the cluster fill counts for each writer in the template training set. First we format the template data to get the cluster fill counts in the proper format for the plotting function.
template_data <- format_template_data(template = template)
plot_cluster_fill_counts(template_data, facet = TRUE)
We will use handwriting samples from each person of interest, calculate the cluster fill counts from each sample using the cluster template, and fit a hierarchical model to estimate each person of interest’s true cluster fill counts.
Save your known handwriting samples from the persons of interest in main_dir \> data \> model_docs as PNG images. The model requires three handwriting samples from each person of interest. Each sample should be at least one paragraph in length. Name the PNG images with a consistent format so that all file names are the same length and the writer ID’s are in the same location. For example, “writer0001_doc1.png”, “writer0001_doc2.png”, “writer0001_doc3.png”, “writer0002_doc1.png”, and so on.
We fit a hierarchical model with the function fit_model. This function does the following:
model_images_dir, decomposing the handwriting into component graphs. The processed graphs are saved in RDS files in main_dir \> data \> model_graphs.In this example, we use 4000 MCMC iterations for the model. The inputs writer_indices and doc_indices are the starting and stopping characters in the model training documents file names that contains the writer ID and a document name.
model <- fit_model(template_dir = "path/to/main_dir",
model_images_dir = "path/to/main_dir/data/model_docs",
num_iters = 4000,
num_chains = 1,
num_cores = 2,
writer_indices = c(7, 10),
doc_indices = c(11, 14))For this tutorial, we will use the small example model, example_model_1chain, included in handwriter. This model was trained from three documents each from writers 9, 30, 203, 238, and 400 from the CSAFE handwriting database.
We can plot the cluster fill counts for each person of interest. (NOTE: We had to format the template data to work with the plotting function, but the model data is already in the correct format.)
The bars across the top of each graph show the Writer ID. Each graph has a line for each known handwriting sample from a given writer.
If you are interested in the variables used by the hierarchical model, continue reading this section. Otherwise, feel free to skip to the next section to learn how to analyze questioned documents.
We can list the variables in the model:
names(as.data.frame(coda::as.mcmc(model$fitted_model[[1]])))
#> [1] "eta[1]" "eta[2]" "eta[3]" "eta[4]" "eta[5]" "eta[6]"
#> [7] "eta[7]" "eta[8]" "eta[9]" "eta[10]" "gamma[1]" "gamma[2]"
#> [13] "gamma[3]" "gamma[4]" "gamma[5]" "gamma[6]" "gamma[7]" "gamma[8]"
#> [19] "gamma[9]" "gamma[10]" "mu[1,1]" "mu[2,1]" "mu[3,1]" "mu[4,1]"
#> [25] "mu[5,1]" "mu[1,2]" "mu[2,2]" "mu[3,2]" "mu[4,2]" "mu[5,2]"
#> [31] "mu[1,3]" "mu[2,3]" "mu[3,3]" "mu[4,3]" "mu[5,3]" "mu[1,4]"
#> [37] "mu[2,4]" "mu[3,4]" "mu[4,4]" "mu[5,4]" "mu[1,5]" "mu[2,5]"
#> [43] "mu[3,5]" "mu[4,5]" "mu[5,5]" "mu[1,6]" "mu[2,6]" "mu[3,6]"
#> [49] "mu[4,6]" "mu[5,6]" "mu[1,7]" "mu[2,7]" "mu[3,7]" "mu[4,7]"
#> [55] "mu[5,7]" "mu[1,8]" "mu[2,8]" "mu[3,8]" "mu[4,8]" "mu[5,8]"
#> [61] "mu[1,9]" "mu[2,9]" "mu[3,9]" "mu[4,9]" "mu[5,9]" "mu[1,10]"
#> [67] "mu[2,10]" "mu[3,10]" "mu[4,10]" "mu[5,10]" "pi[1,1]" "pi[2,1]"
#> [73] "pi[3,1]" "pi[4,1]" "pi[5,1]" "pi[1,2]" "pi[2,2]" "pi[3,2]"
#> [79] "pi[4,2]" "pi[5,2]" "pi[1,3]" "pi[2,3]" "pi[3,3]" "pi[4,3]"
#> [85] "pi[5,3]" "pi[1,4]" "pi[2,4]" "pi[3,4]" "pi[4,4]" "pi[5,4]"
#> [91] "pi[1,5]" "pi[2,5]" "pi[3,5]" "pi[4,5]" "pi[5,5]" "pi[1,6]"
#> [97] "pi[2,6]" "pi[3,6]" "pi[4,6]" "pi[5,6]" "pi[1,7]" "pi[2,7]"
#> [103] "pi[3,7]" "pi[4,7]" "pi[5,7]" "pi[1,8]" "pi[2,8]" "pi[3,8]"
#> [109] "pi[4,8]" "pi[5,8]" "pi[1,9]" "pi[2,9]" "pi[3,9]" "pi[4,9]"
#> [115] "pi[5,9]" "pi[1,10]" "pi[2,10]" "pi[3,10]" "pi[4,10]" "pi[5,10]"
#> [121] "tau[1,1]" "tau[2,1]" "tau[3,1]" "tau[4,1]" "tau[5,1]" "tau[1,2]"
#> [127] "tau[2,2]" "tau[3,2]" "tau[4,2]" "tau[5,2]" "tau[1,3]" "tau[2,3]"
#> [133] "tau[3,3]" "tau[4,3]" "tau[5,3]" "tau[1,4]" "tau[2,4]" "tau[3,4]"
#> [139] "tau[4,4]" "tau[5,4]" "tau[1,5]" "tau[2,5]" "tau[3,5]" "tau[4,5]"
#> [145] "tau[5,5]" "tau[1,6]" "tau[2,6]" "tau[3,6]" "tau[4,6]" "tau[5,6]"
#> [151] "tau[1,7]" "tau[2,7]" "tau[3,7]" "tau[4,7]" "tau[5,7]" "tau[1,8]"
#> [157] "tau[2,8]" "tau[3,8]" "tau[4,8]" "tau[5,8]" "tau[1,9]" "tau[2,9]"
#> [163] "tau[3,9]" "tau[4,9]" "tau[5,9]" "tau[1,10]" "tau[2,10]" "tau[3,10]"
#> [169] "tau[4,10]" "tau[5,10]"View a description of a variable with the about_variable function.
about_variable(variable = "mu[1,1]", model = model)
#> [1] "Mu is the location parameter of a wrapped-Cauchy distribution for writer ID 9 and cluster 1"View a trace plot of a variable.
If we need to, we can drop the beginning MCMC iterations for burn-in. For example, if we want to drop the first 25 iterations, we use
If we want to save the updated model as the current model for this project, replace model.rds in the data folder with
Save your questioned document(s) in main_dir > data > questioned_docs as PNG images. Assign a new writer ID to the questioned documents and name the documents consistently. E.g. “unknown1000_doc1.png”, “unknown1001_doc1.png”, and so on.
We estimate the posterior probability of writership for each of the questioned documents with the function analyze_questioned_documents. This function does the following:
questioned_images_dir, decomposing the handwriting into component graphs. The processed graphs are saved in RDS files in main_dir \> data \> questioned_graphs.main_dir \> data \> questioned_clusters.rds.main_dir \> data \> analysis.rds.analysis <- analyze_questioned_documents(
template_dir = "path/to/main_dir",
questioned_images_dir = "path/to/main_dir/questioned_docs",
model = model,
writer_indices = c(8,11),
doc_indices = c(13,16),
num_cores = 2)Let’s pretend that a handwriting sample from each of the 5 “persons of interest” is a questioned document. These documents are also from the CSAFE handwriting database and have already been analyzed with example_model_1chain and the results are included in handwriter as example_analysis_1chain.
View the cluster fill counts for each questioned document. Intuitively, the model assesses which writer’s cluster fill counts look the most like the cluster fill counts observed in each questioned document.
View the posterior probabilities of writership.
analysis$posterior_probabilities
#> known_writer w0009_s03_pWOZ_r01.png w0030_s03_pWOZ_r01.png
#> 1 known_writer_9 1 0
#> 2 known_writer_30 0 1
#> 3 known_writer_203 0 0
#> 4 known_writer_238 0 0
#> 5 known_writer_400 0 0
#> w0203_s03_pWOZ_r01.png w0238_s03_pWOZ_r01.png w0400_s03_pWOZ_r01.png
#> 1 0.0 0 0
#> 2 0.0 0 0
#> 3 0.3 0 0
#> 4 0.7 1 0
#> 5 0.0 0 1In practice, we would not know who wrote a questioned document, but in research we often perform tests to evaluate models using data where we know the ground truth. Because in this example, we know the true writer of each questioned document, we can measure the accuracy of the model. We define accuracy as the average posterior probability assigned to the true writer. The accuracy of our model is