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Root shape in carrot (Daucus carota subsp. sativus), which ranges from long and tapered to short and blunt, has been used for at least several centuries to classify carrot cultivars. The subjectivity involved in determining market class hinders the establishment of metric-based standards and is ill-suited to dissecting the genetic basis of such quantitative phenotypes. Advances in digital image acquisition and analysis has enabled new methods for quantifying sizes of plant structures and shapes, but in order to dissect the genetic control of the shape features that define market class in carrot, a tool is required that quantifies the specific shape features used by humans in distinguishing between classes. This study reports the construction and demonstration of the first such platform, which facilitates rapid phenotyping of traits that are measurable by hand, such as length and width, as well as principal component analysis (PCA) of the root contour and its curvature. This latter approach is of particular interest, as it enabled the detection of a novel and significant quantitative trait, defined here as root fill, which accounts for 85% of the variation in root shape. Curvature analysis was demonstrated to be an effective method for precise measurement of the broadness of the carrot shoulder, and degree of tip fill; the first principal component of the respective curvature profiles captured 87% and 84% of the total variance. This platform's performance was validated in two experimental panels. First, a diverse, global collection of germplasm was used to assess its capacity to identify market classes through clustering analysis. Second, a diallel mating design between inbred breeding lines of differing market classes was used to estimate the heritability of the key phenotypes that define market class, which revealed significant variation in the narrow-sense heritability of size and shape traits, ranging from 0.14 for total root size, to 0.84 for aspect ratio. These results demonstrate the value of high-throughput digital phenotyping in characterizing the genetic control of complex quantitative phenotypes.