Mathematical Analysis
of “E L I M A R” Inscription

LMI engaged the independent design and technology agency OddCommon, based in New York and London, to undertake a precise mathematical comparison of the letters “E L I M A R” to the block and free form letters found in other autograph works by van Gogh.

The purpose of this analysis was to move beyond the human eye and its naturally associated subjectivity and limitations in precision, and to take an unbiased, data-led approach.

The following pages set forth the process OddCommon followed, the data set from which its analysis began, the data it utilized based on the quality of images, the scale of its undertaking, and the mathematically accurate comparative visualizations that resulted.

The Appendix of LMI's Report reproduces the entirety of the raw data and computational methodologies that sit behind the summary provided provided below.

Vincent van Gogh, Elimar, 1889, Saint-Rémy-de-Provence, oil on canvas, 45.7 x 41.9 cm, Inscribed lower right, “ELIMAR.” Owner, LMI Group International, Inc., SPV Number 0719 LLC.

The data set

Van Gogh's known body of work provided a range of letterforms and words to compare to ELIMAR. Of these works, twelve were selected based on the presence of capital letters and our ability to obtain reliable measurements.

Normalizing the data

In the 12 selected artworks where suitable comparative letterforms were found, these letterforms were painted with various sizes, angles and perspectives.

We created a normalization process to extract the letterform, adjust to a flat front perspective, enhance resolution where necessary, and then create various versions of the letterform that could be accurately measured.

Once all the letterforms were normalized in the same control area, we used a relative decimal point measurement system to take measurements with high precision.

Measurement

To measure the attributes of each letter we leaned into traditional typography and its well-established taxonomy around letterforms.

We also used the Hausdorff measurement, which is a way of comparing how close or far apart two shapes are. For any two shapes, it tells you the largest and closest possible distance between any point.

This measurement is useful when comparing shapes using computer vision, when you want to know how similar or different two objects are.

In addition to character analysis, we also performed analysis on full words. Here we show the letter angle between ELIMAR and the words EMILE ZOLA from the painting Still Life with Bible (1885).

Addressing technical challenges in the arts and cultural heritage sector

This investigation exemplifies LMI’s approach to tackling specific data challenges in the arts and cultural heritage sector.